(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Biodiversity Heritage Library | Children's Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "The life of John Dollond, F. R. S., inventor of the achromatic telescope, with a copious appendix of all the papers referred to"

m^ 



r^ r' 



W 









1808 




• IIKIII 

.IBRARY 

INIVERSITY or 
CALIFORNIA 



^ I <^ ^ ^^ , ^ ^ 




It 

^ C>K.U,^ -710 , JCL^ '<^^3. 



JO^ 



,4..t-t^A^^ U -y.-^- '-y -/ ' '^"- •-■ 






.Ju^'/P^ 



i^y ^-^ 



FromdfcMfeof 




F(?flov^of tfic Royaf Society 




# 



# 



m^ 






% 



*** 



M 



.«■» 



r^ 




Engruyed: ^ J.Pofieiwhii& 



B(Q)j! 



:o) 



• ,,.,// r '''/i/y/ ?/ 



4 



t 



^# 



'lln 



I'fV f>l li.r OltTllSLim uf I).-;cfiil Knowlrilt; 



■,jA/ Ludn.u. <H-atAl:,l< M.ill I-:. 




THE 

LIFE 

OF 

JOHN DOLLOND, F.R.S. 

INVENTOR 

OF THE 

^c!)romatit Celesrope. 



With a copious Appendix of all the Papers referred to. 



BY 

JOHN KEJLJLY, ILIL.B. 

RECTOR OF COPFORD, IN THE COUNTY OF ESSEX ; , 

Author of the Triglott Celtic Dictionary, and a Translator of the 
Bible into the Manks Gaelic. 



THIRD EDITION WITH ADDITIONS. 



PRINTED BY W. M. THISELTON, 37, GOODGE STRKE'[ 



1808. 



LOAN STACK 






CONTENTS 



Page 
TAeXj/eo/JohnDollond, F.R.S 5 

u4 Letter from Mr. John Dollond to Mr. James Short, F.R.S. con- 
cerning an Improvement of Refracting Telescopes . . . . 17 

Letters relating to a Theorem of M. Euler, of the Royal Academy of ' 
Sciences at Berlin, and F.R.S. for correcting the Aberrations in 
the Object-Glasses of Refracting Telescopes •. ^1 

~/i Description of a Contrivance Jbr Measuring Small Angles, bi/ 
Mr. John Dollond; communicated by Mr. J. Short, F.R.S. . 33 

An Explanation of an Instrument for Measuring Small Angles, the 

first Account of which was read before the Royal Society, May 10, 

1753. By Mr. John Dollond. In a Letter to James Short, M. A. 

and F.R.S 36 



433 



11 CONTENTS. 

/ 

Page 
An jiccount of some Experiments concerning the different Refrangibility 

of Light. By Mr. John Dollond. With a Letter from James 

Short, M.A. F.R.S. Acad. Reg. Suec. Soc. 50 

Some Account of the Discovery, made by the late Mr. John Dollond^ 
F.R.S. which led to the grand Improvement o/" Refracting Teles- 
copes, in order to correct some Misrepresentations, in Foreign 
Publications, of that Discovery: with an Attempt to account for the 
Mistake in an Experiment made by Sir Isaac Newton ; on ivhich 
Experiment, the Improvement of the Refracting Telescope intirely 
depended, By Peter Dollond, Member of the American Philoso- 
phical Society at Philadelphia 6l 

An Attempt to explain a Difficulty in the Theory of Vision, depending 
on the different Refrangibility of Light. By the Rev. Nevil Maske- 
lyne, D.D. F.R.S. and Astronomer Royal 78 

An Account of an Improvement made by Mr. Peter Dollond in his New 
Telescopes. In a Letter to James Short, M.A. F.R.S. tvith a 
Letter of Mr. Short^o the i2e?;. Thomas Birch, D.D. fe.R.S. 8 8 

A Letter from Mr. Peter Dollond, to Nevil Maskelyne, F.R.S. and 
Astronomer Royal; describing some Additions and Alterations made 
to Hadley's Quadrant, to render it more serviceable at- Sea . 92 

Remarks on the Hadley's Quadrant, tending principally to remove the 
Difficulties which have hitherto attended the Use of the Back-^observa- 



CONTENTS. Ill 

Page 
tion, and to obviate the Errors that might arise from a JVant of 

Parallelism in the two Surfaces of the Index-Glass. By Nevil 

Maskelyne, F. R. S. Astronomer Royal 9^ 

An Account of an Apparatus applied to the Equatorial Instrument for 

, correcting the Errors arising from the Refraction in Altitude. By 

Mr. Peter Dollond, Optician; communicated to the Royal Society 

by the Astronomer Royal .119 



A 'I 



THE 



LIFE 



OF 



JOHN DOLLOND, F.R.S. 



In modem times the attention of men has been employed rather in 
improving what they know than in attempting to make new disco- 
veries. When a man, therefore, has been fortunate enough, by 
extraordinary research, or by a strong effort of genius, to surprise 
the world with a new invention, a lively interest is immediately excited 
in every mind to trace the steps, investigate the means, and collect 



6 ' LIFE OF JOHN DOLLONp, F.R.S. 

every incident which led to the result: — and to the honour of human 
nature be it said, while curiosity exerts itself in this manner on the 
invention, the inventor is not less the object of regard and consi- 
deration: we wish to learn the history, the life, the character of the 
man, and, as far as it is possible, to be acquainted with him. The 
subject of the following memoir is entitled to this introduction, and 
the public will receive with satisfaction the following account of the 
inventor of the achromatic telescope. 

John Dollond, fellow of the Royal Society, was born in Spitalfields, 
I J Oh on the tenth day of June in the year 1706: his parents were French 

protestants, and at the time of the revocation of the ^dict of Nantz, 
which happened in the year l685, resided in Normandy; but in what 
particular part of it is not at present precisely known : M. de Lalande 
does not believe the name to be of French origin : but however this may 
be, the family were compelled soon after this period to seek refuge in 
England, in order to avoid persecution and to preserve their religion. 

The fate of this family was not a solitary case; fifty thousand per- 
sons pursued the same measures, and we may date from this period 
the rise of several arts and manufactures, which have become highly 
beneficial to this country. An establishment was given to these 
refugees, by the wise policy of our government, in Spitalfields, and 
particular encouragement granted to the silk manufactory. 

The first years of Mr. Dollond's life were employed at the loom; 
but, being of a very studious and philosophic turn of mind, his leisure 
hours were engaged in mathematical pursuits; and though by the 
death of his father, which h ippened in his infancy, his education 
gave way to the necessities of \ is family, yet at the age of fifteen. 



LIFE OP JOHN DOLLONDj F.R.S. 7 

before he had an opportunity of seeing works of science or elementary 
treatises, he amused himself by constructing sun-dials, drawing geo- 
metrical schemes, and solving problems. 
'^* 'An early marriage and an increasing family afforded him little 
opportunity of pursuing his favourite studies: but such are the powers 
of the human mind when called into action, that difficulties, which 
appear to the casual observer insurmountable, yield and retire before 
perseverance and genius: even under the pressure of a close applica- 
tion to business for the support of his family, he found time, by 
abridging the hours of his rest, to extend his mathematical knowledge, 
and made a considerable proficiency in optics and astronomy, to which 
he now principally devoted his attention, having in the earlier stages 
of his life prepared himself for the higher parts of those subjects by 
a perfect knowledge of algebra and geometry. 

Soon after this, without abating from the ardour of his other lite- 
rary pursuits, or relaxing from the labours of his profession, he began 
to study anatomy, and likewise to read divinity; and finding the 
knowledge of Latin and Greek indispensably necessary towards at- 
taining those ends, he applied himself diligently, and was soon able 
to translate the Greek Testament into Latin ; and as he admired the 
power and the wisdom of the Creator in the mechanism of the 
human frame, so he adored his goodness displayed in his revealed 
word. 

It might from hence be concluded that his sabbath was devoted to 
retired reading and philosophical objects; but he was not content with 
private devotion, as he was always an advocate for social worship, and 
with his family regularly attended the public service of the French 



8 LIFE OF JOHN DOLLOND, P.R.S. 

protestant church, and occasionally heard Benson and Lardner, whom 
he respected as men and admired as preachers. In his appearance he 
was grave, and the strong lines of his face were marked with deep 
thought and reflection; but in his intercourse with his family and 
friends, he was cheerful and affectionate; and his language and senti- 
ments are distinctly recollected as always making a strong impression 
on the minds of those with whom he conversed. His memory was 
extraordinarily retentive, and, amidst the variety of his reading, he 
could recollect and quote the most important passages of every book 
which he had at any time perused. 

He designed his eldest son, Peter Dollond, for the same business 
with himself; and for several years they carried on their manufactures 
together in Spitalfields ; but the employment neither suited the ex- 
pectations nor disposition of the son, who, having received much 
information upon mathematical and philosophical subjects from the 
instruction of his father, and observing the great value which was set 
upon his father's knowledge in the theory of optics by professional 
men, determined to apply that knowledge to the benefit of himself 
and his family; and accordingly, under the directions of his father, 
commenced optician. Success, though under the most unfavourable 
circumstances, attended every effort; and in the year 1752 John Dol- 
lond, embracing the opportunity of pursuing a profession congenial 
with his mind, and without neglecting the rules of prudence towards 
his family, joined his son, and in consequence of his theoretical 
knowledge, soon became a proficient in the practical parts of optics. 

His first attention was directed to improve the combination of the 
eye-glasses of refracting telescopes; and having succeeded in his sys- 



LIFE OP JOHN DOLLOND, P.K.S. 9 

tem of four eye-glasses, he proceeded one step further, and produced 
telescopes furnished with five eye-glasses, which considerably surpassed 
the former; and of which he gave a particular account in a paper 
presented to the Royal Society, and which was read on the 1st of 
March 1753, and printed in the Philosophical Transactions, vol. 
xlviii. page 108. — See appendix, pp. 17 — 20. 

Soon after this he made a very useful improvement in Mr. Savery's 
micrometer: for instead of employing two entire object-glasses, as 
Mr. Savery and M. Bouguer had done, he used only one glass cut 
into two equal parts, one of them sliding or moving laterally by the 
other. This was considered to be a great improvement, as the mi- 
crometer could now be applied to the reflecting telescope with much 
advantage, and which Mr. James Short immediately did. An account 
of the same was given to the Royal Society, in a paper which was 
afterwards printed in the Philosophical Transactions, vol. xlviii. page 
178; and in another paper, part ii. page 551. — See appendix, pp. 
33 — 49.* 

Mr. Dollond's celebrity in optics became now universal; and the 
friendship and protection of the most eminent men of science flattered 
and encouraged his pursuits. To enumerate the persons, both at 
home and abroad, who distinguished him by their correspondence or 
cultivated his acquaintance, however honourable to his memory, 
would only be an empty praise. We cannot, however, forbear men- 



* This kind of micrometer was afterwards applied by Mr. P. DoUond to the achro- 
matic telescope.— /See Appendix^ pp. 88 — ^91. 

B 



10 LIFE OP JOHN DOLLOND, F.R.S. . 

tigning the names of a few persons, who held the highest place in 
his esteem as men of worth and learning: — Mr. Thomas Simpson, 
master of the Royal Academy at Woolwich; Mr. Harris, assay- 
master at the Tower, who was at that time engaged in writing and 
publishing his Treatise on Optics; the Rev. Dr. Bradley, then astro- 
nomer royal; the Rev. William Ludlam, of St. John's college, Cam- 
bridge; Mr. John Canton, a most ingenious man, and celebrated 
not less for his knowledge in natural philosophy, than for his neat 
and accurate manner of making philosophical experiments. To this 
catalogue of the philosophical names of those days, we must add that 
of the present astronomer royal, the Rev. Dr. Maskelyne, whose 
labours have so eminently benefited the science of astronomy. 

Surrounded by these enlightened men, in a state of mind prepared 
for the severest investigation of philosophic truths, and in circum- 
stances favourable to liberal inquiry, Mr. Dollond engaged in the 
discussion of a subject, which at that time not only interested this 
country, but all Europe. Sir Isaac Newton had declared, in his Trea- 
tise on Optics, page 112, " That all refracting substances diverged 
the prismatic colours in a constant proportion to their mean re- 
fraction;" and drew this conclusion, " that refraction could not be 
produced without colour;" and consequently, " that no improvement 
could he expected in the refracting telescope.'" No one doubted the 
accuracy with which Sir Isaac Newton had made the experiment; yet 
some men, particularly M. Euler and others, were of opinion that 
the conclusion which Newton had drawn from it went too far, and 
maintained that in very small angles refraction might be obtained 
without colour. Mr. Dollond was not of that opinion, but defended 



LIFE OP JOHN DOLLOND, F.R.S. 11 

Newton's doctrine with much learning and ingenuity, as may be seen 
by a reference to the letters which passed between Euler and Dollond 
upon that occasion, and which were published in the Philosophical 
Transactions, vol. xlviii. page 287 — see Appendix, pp. 21 — 32; and 
contended that, " If the result of the experiment had been as de- 
scribed by Sir Isaac Newton, there could not be refraction without 
colour." 

A mind constituted like Mr. Dollond's could not remain satisfied 
with arguing in this manner from an experiment made by another, 
but determined to try it himself, and accordingly, in the year 1757, 
began the examination ; and, to use his own words, with, " a resolute 
perseverance," continued during that year, and a great part of the 
next, to bestow his whole mind on the subject, until in the month 
of June 1758 he found, after a complete course of experiment, the 
result to be very different from that which he expected, and from that 
which Sir Isaac Newton had related. He discovered " the difference 
in the dispersion of the colours of light, when the mean rays are equally 
refracted hy different mediums.''^ The discovery was complete, and he 
immediately drew from it this practical conclusion, '^ That thQ object- 
glasses of refracting telescopes were capable of being made without 
the images formed by them being affected by the different refrangi- 
bility of the rays of light." His account of this experiment, and of 
others connected with it, was given to the Royal Society, and printed 
in their Transactions, vol. I. page 743 — see Appendix, pp, 50 — 60; 
and he was presented in the same year, by that learned body, with 
Sir Godfrey Copley's medal, as a reward of his merit, and a memorial 
of the discovery, though not at that time a member of the society. 

B 2 



12 LIFE OF JOHN DOLLOND, P.R.S, 

This discovery no way affected the points in dispute between Euler 
and Dollond, respecting the doctrine advanced by Sir Isaac Newton.* 
A new principle was in a manner found out, which had no part in 
their former reasonings, and it was reserved for the accuracy of Dol- 
lond to have the honour of making a discovery which had eluded the 
observation of the immortal Newton. -{- 

This new principle being now established, he was soon able to con- 
struct object-glasses, in which the different refrangibility of the rays 
of light was corrected, and the name of achromatic given to them by 
the late Dr. Bevis, on account of their being free from the prismatic 
colours. Dr. Hutton, in his Mathematical Dictionary, has said that 
this name was given to them by M. de Lalande; but that is a mistake. 

As usually happens on such occasions, no sooner was the achro- 
matic telescope made public, than the rivalship of foreigners, and 
the jealousy of philosophers at home, led them to doubt of its 
reality; and Euler himself, in his paper read before the Academy of 
Sciences at Berlin, in the year 17^4, says, " I am not ashamed 
frankly to avow, that the first accounts, which were published of it, 
appeared so suspicious, and even so contrary to the best established 
principles, that I could not prevail upon myself to give credit to them ;" 



* See note at bottom of pages 79 — 80, for Priestley's remarks, &c, 
t The cause of this difference of the results of the 8th experiment of the 2nd part 
of the first book of Newton's Optics, as related by himself, and as it was found when 
tried by DoUond in the years 1757 and 1758, is fully and ingeniously accounted for by 
Mr. Peter DoUond in a paper read at the Royal Society on the 21st of May 1789, and 
afterwards published for J. Johnson in St. Paul's Church Yard-— 5ee Appendix, pp.QX—^ 
yy ; also in Hutton's Dictionary— Article, Chromatic. 



WPE OP JOHN DOLLOND, P.R.&. 13 

and he adds, " I should never have submitted to the proofs which 
Mr. Dollond produced to support this strange phaenomenon, if M. 
Clairaut, who must at first have been equally surprized at it, had not 
most positively assured me that Dollond's experiments were but too 
well founded." And when the fact could no longer be disputed,, they 
endeavoured to find a prior inventor, to whom it might be ascribed, 
and several conjecturers were honoured with the title of discoverers. 

Mr. Dollond's improvement in refracting telescopes was of the 
greatest advantage in astronomy, as they have been applied to fixed 
instruments; by which the motions of the heavenly bodies are de- 
termined to a much greater exactness than by the means of the old 
telescope. Navigation has also been much benefited by applying 
achromatic telescopes to the " Hadley's sextant:" and from the im- 
proved state of the lunar tables, and of that instrument, the longitude 
at sea may now be determined by good observers to a great degree of 
accuracy; and their universal adoption by the navy and army, as well 
as by the public in general, is the best proof of the great utility of 
the discovery. 

In the beginning of the year 1761, Mr. Dollond was elected fellow 
of the Royal Society, and appointed optician to his majesty, but did 
not live to enjoy those honours long; for on the 30th of November, 
in the same year, as he was reading a new publication of M. Clairaut, 
on the theory of the moon, and on which he had been intently en- 
gaged for several hours, he was seized with apoplexy, which rendered 
him immediately speechless, and occasioned his death in a few hours 
afterwards. Besides Mr. Peter Dollond, whom we had occasion to 
mention in this memoir, his family, at his death, consisted of three 



14 LIFE OP JOHN DOLLONDj F.R.S, 

daughters and a son, who, possessing the name of his father, and 
we may add, a portion of the family abilities, carried on the optical 
business in partnership with his elder brother. 

Since the last edition of this Life, we have to mention the death 
of Mr. John Dollond, the partner of, his elder brother Mr. Peter 
DoUond, which has occasioned the latter to take into partnership his 
nephew, the son of his eldest sister, Mr. George Huggins, who has, 
by the King's permission, taken the name of Dollond. 



THE END OP THE LIFE. 



THE APPENDIX. 



■ii 



APPENDIX. 



A Letter from Mr, John DoUond to Mr. James 
Short, F.R S. concerning an Improvement of 
Refracting Telescopes. 

Read March 1, 1753. 

SIR, 

JLT is well known, that the perfection of refracting 
telescopes is very much limited by the aberration of the rays of light 
from the geometrical focus; which arises from two very different causes; 
that is, from different degrees of refrangibility of light, and from the 
figure of the sphere, which is not of a proper curvature for collecting 
the rays in a single point. The object-glass is chiefly affected by the 
first of these; nor has there been yet any method discovered for recti- 
fying that aberration so, as in the least to remove the indistinctness of 
the image arising from it. We are therefore reduced to the necessity 
of contracting their apertures, which renders it impossible to magnify 
much without very long glasses. 

c 



18 A Letter from Mr, John Dollond to Mr. James Short, 

But the case is widely different with regard to the eye-glasses; for, 
though they are very much affected by both the aberrations before- 
mentioned, yet, by a proper combination of several together, their 
errors may be in a great measure corrected. If any one, for instance, 
would have the visual angle of a telescope to contain 20 degrees, the 
extreme pencils of the field must be bent or refracted in an angle of 
10 degrees; which, if it be performed by one eye-glass, will cause 
an aberration from the figure, in proportion to the cube of that angle: 
but if two glasses are so proportioned and situated, as that the re- 
fraction may be equally divided between them, they will each of them 
produce a refraction equal to half the required angle: and therefore 
the aberration being in proportion to the cube of half the angle taken 
twice over, will be but a fourth part of that, which is in proportion 
to the cube of the whole angle; because twice the cube of one is but 
J of the cube of two; so the aberration from the figure, where two 
eye-glasses are rightly proportioned, is but a fourth of what must 
unavoidably be, where the whole is performed by a single eye-glass. 
By the same way of reasoning, when the refraction is divided between 
three glasses, the aberration will be found to be but the ninth part of 
what would be produced from a single glass; because three times the 
cube of one is but one ninth of the cube of 3. Whence it appears, 
that, by increasing the number of eye-glasses, the indistinctness, 
which is observed near the borders of the field of a telescope, may 
be very m;ich diminished, though not intirely taken away. 

The method of correcting the errors arising from the different 
refrangibility of light is of a different consideration from the former; 
for, whereas the errors from the figure can only be diminished in a 



concerning an Improvement of Refracting Telescopes, 19 

certain proportion to the number of glasses, in this they may be 
intirely corrected, by the addition of only one glass; as we find in 
the astronomical telescope, that two eye-glasses, rightly proportioned, 
will cause the edges of objects to appear free from colours quite to 
the borders of the field. Also in the day telescope, where no more 
than two eye-glasses are absolutely necessary for erecting the object, 
we find, by the addition of a third rightly situated, that the colours, 
which would otherwise confuse the image, are intirely removed: — I say 
intirely removed; but this is to be understood with some limitation; 
for though the different colours, which the extreme pencils must 
necessarily be divided into by the edges of the eye-glasses, may in this 
manner be brought to the eye in a direction parallel to each other, so 
as, by the humours thereof, to be converged to a point in the retina; 
yet, if the glasses exceed a certain length, the colours may be spread 
too wide to be capable of being admitted through the pupil or aperture 
of the eye; which is the reason, that, in long telescopes, constructed 
in the common manner, with three eye-glasses, the field is always 
very much contracted. 

These considerations^ Sir, first set me on contriving, how to en- 
large the field by increasing the number of eye-glasses, without any 
hinderance to the distinctness or brightness of the image: and though 
others had been about the same work before, yet observing, that the 
five-glass telescopes, sold in the shops, would admit of farther im- 
provement, I endeavoured to construct one with the same number of 
glasses in a better manner; which so far answered my expectations, as 
to be allowed by such persons, as are the best judges, to be a consi- 
derable improvement on the former. 

c 2 



20 A Letter from Mr. John Dollond to Mr. James Short, &c. 

Encouraged by this success, I resolved to try, if possibly I might 
gain some farther enlargement of the field by the addition of another 
glass; and by placing and proportioning the glasses in such a manner, 
as to correct the aberrations as much as possible, without any 
detriment to the distinctness, I have obtained as large a field, as is 
convenient or necessary, and that even in the longest telescopes, 
which can be made. 

These telescopes with six glasses having been well received, and 
some of them being gone to foreign parts, it seems a proper time to 
settle the account of its origin; which is one of the motives, that has 
induced me to trouble you with this short sketch of the considerations, 
that gradually led me to its construction ; and I am emboldened. Sir, 
to write thus much, from the many favours I have already received at 
your hands, as well as from a sense of your being a proper person to 
judge in such cases. And though I am sensible, that you are not 
unacquainted with the theory contained in this letter, yet forasmuch 
as the subject has never been fully treated by any author, I shall en- 
deavour, as soon as may be, to draw up a more particular explanation 
of the aberrations of light by refraction; but shall add no more at 
present, only beg leave to take this opportunity of subscribing 
myself 

Your much obliged 

and most humble servant^ 

John Dollond. 

Vine Court, 
February 21, 1753. 



21 



Letters relating to a Theorem of Mr. Euler, of 
the Royal Academy of Sciences at Berlin, and 
F.R.S. for correcting the Aberrations in the 
Object-Glasses of Refracting Telescopes. 



No. 1. 
A Ze«er/rom Mr. James Short, F.R.S. to Peter Duval, Esq. F.R.S. 

Read April 9, 1752. 

DEAR SIR, 

1 HERE is published, in the Memoirs of the Royal 
Academy at Berlin, for the year 1747, a theorem by Mr. Euler, in 
which he shews a method of making object-glasses of telescopes, in 
such a manner, as not to be affected by the aberrations arising from 
the different refrangibility of the rays of light: these object-glasses 
consisting of two meniscus lenses, with water between them. 

Mr. John Dollond, who is an excellent analyst and optician, has 
examined the said theorem, and has discovered a mistake in it, which 
arises by assuming an hypothesis contrary to the established principles 
of optics; and, in consequence of this, Mr. Dollond has sent me 



11 Letters relating to a Theorem, 8$c. 

the inclosed letter, which contains the discovery of the said mistake, 
and a demonstration of it. 

In order to act in the most candid manner with Mr. Euler, I have 
proposed to Mr. DoUond to write to him, shewing him the mistake, 
and desiring to know his reasons for that hypothesis; and therefore I 
desire, that this letter of Mr. Dollond's to me may be kept amongst 
the Society's papers, till Mr. Euler has had a sufficient time to 
answer Mr, Dollond's letter to him. -i-s-'., «|'>'^ 

I am, SIR, 

Your most humble servant, 

James Shoit. 

Surrey Street, 
April 9, 1752. 



.nnr^- n 



of Mr, Euler, of the Royal Academy of Berlin, 23 



No. 2. 

A Letter from Mr. John Dollond to James Short, A.M. F.R.S. 
concerning a Mistake in M. Euler's Theorem for correctirig the 
Aberrations in the Object-Glasses of Refracting Telescopes. 

Read November 23, 1752. 

SIR, 

1 HE famous experiments of the prism, first tried 
by Sir Isaac Newton, sufficiently convinced that great man, that the 
perfection of telescopes was impeded by the different refrangibility of 
the rays of light, and not by the spherical figure of the glasses, as 
the common notion had been till that time; which put the philoso- 
pher upon grinding concave metals, in order to come at that by 
reflection, which he despaired of obtaining by refraction. For, that 
he was satisfied of the impossibility of correcting that aberration by a 
multiplicity of refractions, appears by his own words, in his Treatise 
of Light and Colours, Book I. Part 2. Prop. 3. " I found more- 
" over, that when light goes out of air through several contiguous 
" mediums, as through water and glass, as often as by contrary 



24 Letters relating to a Theorem^ ^c. 

" refractions it is so corrected, that it emergeth in lines parallel to 
" those in which it was incident, continues ever after to be white. 
" But if the emergent rays be inclined to the incident, the whiteness 
" of the emerging light will by degrees, in passing on from the place 
" of emergence, become tinged in its edges with colours." 

It is therefore, Sir, somewhat strange, that any body now-a-days 
should attempt to do that, which so long ago has been demonstrated 
impossible. But, as so great a mathematician as Mr. Euler has lately 
published a theorem * for making object-glasses, that should be free 
from the aberration arising from the different refrangibility of light, 
the subject deserves a particular consideration. I have therefore care- 
fully examined every step of his algebraic reasoning, which I have 
found strictly true in every part. But a certain hypothesis in page 
285, appears to be destitute of support either from reason or experi- 
ment, though it be there laid down as the foundation of the whole 
fabriek. This gentleman puts m : 1 for the ratio of refraction out of 
air into glass of the mean refrangible rays, and M'. 1 for that of the 
least refrangible. Also for the ratio of refraction out of air into 
water of the mean refrangible rays he puts nil, and for the least 
refrangible N'.l, As to the numbers, he makes w=-|-i., JW=xi=^ 
and n=4-; which so far answer well enough to experiments. But 
the difficulty consists in finding the value of N in a true proportion 
to the rest. 

Here the author introduces ' the supposition above-mentioned ; 

* Vide Memoirs of the Royal Academy of Berlin for the Year 1747' 



of Mr, Euler, of the Royal Academy of Berlin. 25 

which is, that m is the same power of M, as n is of N; and therefore 
puts n=:m^, and N=M^. Whereas, by all the experiments that have 
hitherto been made, the proportion will come out thus, m—l: 
n—1: :m—M:n—N. 

The letters fixed upon by Mr. Euler to represent the radii of the 
four refracting surfaces of his compound object-glass, ^refg h and k, 
and the distance of the object he expresses by a; then will the focal 

distance be= J ^ . Now, says he, 

w(7— t) +^(7— 7-tt— t; — t— / "TT 

it is evident, that the different refrangibility of the rays would make 
no alteration, either in the place of the image, or in its magnitude, 
if it were possible to determine the radii of the four surfaces, so as to 

have n(t-i)+m(^-t+i-i) = ^(7-i)+M7-t+i-i-)- And 
this. Sir, I shall readily grant. But when the surfaces are thus 
proportioned, the sum of the refractions will be=0; that is to say, 
the emergent rays will be parallel to the incident. For, if w(-^— x) + 

• Mi— 7+i-i) =iV(t-i)+i^i'(:^-t+i-i). thenn^N{^^^)^ 
w_3f (i— -i:-j-L«.x)=0. Also if n—Nim—M: :w— 1 :7ra— 1, then 

w-l(t-i)+w-l(:^-t+i-i)=0; or otherwise ?2(t~i)+w,(;^-t 
Hhi— i")— /+i=0; which reduces the denominator of the fraction 
expressing the focal distance to -^. Whence the focal distance will be 
= a; or, in other words, the image will be the object itself. And as, 
in this case, there will be no refraction, it will be easy to conceive 
how there should be no aberration. 

And now. Sir, I think I have demonstrated, that Mr. Euler's 
theorem is intirely founded upon a new law of refraction of his awn ; 
but that, according to the laws discovered by experiment, the 



26 



Letters relating to a Theorem, 8^c. 



aberration arising from the different refrangibility of light at the 
object-glass cannot be corrected by any number of refractions 
whatsoever. 



London, 
March 11, 3752, 



I am, SIR, 

Your most obedient humble servant, 

John DoUond. 



of Mr, Euler, of the Royal Academy of Berlin. ^ 

^ No. 3. 

Mr. Euler's Letter to Mr. James Short, F.R.S. 
Read Jvdy 8, 1753. 

MONSIEUR, 

V OUS m'avez fait un tres sensible plaisir, ent g.yant 
dispose M. Dollond de remettre la proposition de ses objections 
contre mes verres objectifs, jusqu' k ce que j'y aurois repondu, et je 
vous en suis infininient oblige. Je prend done la liberte de vous 
addresser ma reponse k lui, en vous priant, apres I'avoir daignee de 
votre examen, de la vouloir bien lui remettre: et en cas que vous 
jugiez cette matiere digne de I'attention de la Societe Royale, je vous 
prierois de lui communiquer les preuves detaillees de ma theorie, que 
j'ai exposee dans cette lettre. Cependant j'espere, que M. Dollond en 
sera satisfait, puisque je tombe d'accord avec lui du pen de succes, 
qu'on sauroit se promettre de mes objectifs, en les travaillant selon la 
maniere ordinaire. 

J'ai I'honneur d'etre, avec la plus parfaite consideration, 

MONSIEUR, 

Votre tres humble, et 

tres obeissant serviteur, 

L. Euler. 

Berlin, 
Juin IQ, iy5'J>. 

D '2 



28 Letters relating to a Theorem, 8^e, 



No. 4. 

^ Monsieur Monsieur Dollond. 
Read July 8, 1753. 

MONSIEUR, 

JjiTANT tres sensible a I'honneur qu6 vous me faites, 
au sujet des verres objectifs, que j'avois propose, j'ai celiii de vous 
marquer d'abord ingenument, que j'ai rencontre aussi ici le plus 
grands obstacles dans I'execution de ce dessein, vu qu'il s'agit de 
quatre faces, qui doivent etre travaillee exactement selon les propor- 
tions que j'avois trouvees : cependant ayant fait les- experiences sur 
quelquesuns, qui parurent le mieux reussi^ nous avons trouv^, que 
I'intervalle entre les deux foyers des rayons rouges et violets etoit 
beaucoup plus petit, qu'il ne seroit d'un verre simple de la meme 
distance focale. Neantmoins je dois avoiier, qu'un tel verre, quand 
meme il bien seroit parfaitement execute sur mes principes, auroit 
d'autres defauts, qui le mettroient au dessous meme des verres ordi- 
naires : c'est qu'un tel verre n'admet qu'un tres petite ouverture en 
consequence des grandes courbures, qu'on doit donner aux faces in- 
terieures: desorte que lorsqu'on donne une ouverture ordinaire, 
I'image devient tres confus. 



of Mr. Elder J of the Royal Academy of Berlin^ ^9 

Ainsi puisque vous vous etes donne la peine, Monsieur, d*executer 
de tels verres, en en faisant des experiences*, je vous prie de bien 
distinguer les defauts. qui peuvent naitre de* la diverse refrangibilit6 
des rayons, de ceux, qui viennent d'une trop grande ouverture: pour 
cet efFet vous n'aurez qu'a laisser une tres petite ouverture. 

Or si ma theorie etoit juste, dont j'aurai bientot I'honneur de 
parler, il seroit moyen de remedier k ce defaut; il faudroit renoncer a 
la figure spherique qu'on donne ordinairement aux faces des verres, et 
tacher de leur donner une autre figure, et j'ai remarque que la figure 
d'une parabole leur procureroit Tavantage, qu'ils admettroieiit une 
ouverture tres considerable. Notre savant M. Lieberkuhn s'est appli- 
que ^ travailler des verres dont la courbure des faces decroit depuis le 
milieu vers le bords, et il s'en est aperqu de tres grands avantages. 
Par ces raisons je crois, que ma theorie ne soufFre encore rien de ce 
cotd. 

Pour la theorie, je conviens avec vous, monsieur, que posant la 
raport de refraction d'un milieu dans un autre quelconque pour les 
rayons moyens comme w ^ 1, et pour les rayons rouges comme il/ a 1, 
la raison de m — M ^ m — 1 sera toujours si ^ peu pres constant, 
qu'elle satisfera a toutes les experiences, comme la grand Newton a 
remarque. Cette raison ne difFere non plus de ma theorie que 
presque imperceptiblement: car puisque je soutiens que ilf=w*, et 
que m difFere ordinairement fort peu de I'unite, soit m=^\-\-.:; et 



* Mr. Dollond, in his letter to Mr. Euler, here referred to, does not say that he had 
made any trials himself, but only he had vmderstood that such had been naade by othersj 
without success. 



30 Letters relating to a Theorem^ S^c. 

puisque M=w*=l+a I m ^ peu pres, et I (i+w)=/7W=rw, aussi fort 
i peu pres, j'aurai 7w~il:f=l+w-rl-acd= (l~*) w, et m-l = 6<j, done 

la raison —11^ — sera=l— a, ou fort a pea pres constante, Del^ ie 
w— I ^ •* 

conclude que les experiences d'ou le grand Newton a tire son raport, 
ne sauroient etre contraires k ma theorie. 

En second lieu, je conviens aussi que si la raison —^^^^^^^ — = Const. 

m — I 

fetoit juste k la rigueur, il n'y auroit plus moyen de remedier au 
defaut qui resulte de la diverse refrangibilite des rayons, de quelque 
maniere qu'on disposeroit divers milieux transparens, et que I'intervalle 
entre les divers foyers tiendroit toujours un raport constant a la dis- 
tance focale entiere du verre. Mais c'est precisement cette consi- 
deration, qui me fourriit le plus fort argument: I'oeil me paroit une 
telle machine dioptrique parfaite, qui ne se ressent en aucune maniere 
de la diverse refrangibilite des rayons: quelque petite que soit sa 
distance focale, la sensibilite est si grande, que les divers foyers, s'il y 
en avoit, ne manqueroient pas de troubler tres considerablement la 
vision. Or il est bien certain, qu'un oeil bien constitue ne sent point 
I'eiFet de la diverse refrangibilite. 

La structure merveilleux de Toeil, et les diverses humeurs^ dont il 
est compose, me confirme infiniment dans ce sentiment. Car s'il 
s'agissoit seulement de produire une representation sur le fond de 
Toeil, une seulehumeur auroit ete suffisante; et le Createur n'y auroit 
pas surement employe plusieurs. Dela je conclud, qu'il est possible 
d' aneantir I'effet de la diverse refrangibilite des rayons par une juste 



of Mr. Euler, of the Royal Academy of Berlin, 3 1 

arrangement de plusieurs milieux transparens, done puisqiie cela ne 

seroit pas possible, si la formule— ^^^^ — = Const, etoit vraye a la ri- 

m — 1 

gueur, j'en tire la consequence qu'elle n'est pas parfaitement conforme k 

la nature. 

Mais voila une preuve directe de ma these: je conqois diverse 
milieuz transparens, A, B, C, D, E, S^c. qui different entr'eux egale- 
ment par raport a leur densite optique: desorte que la raison de 
refraction de chacun dans le suivant soit le meme. Soit done dans le 
passage du premier dans le second la raison de refraction pour les 
rayons rouges=r: 1, et pour les violets=i;: 1 ; qui sera la meme dans 
le passage du second dans le troisieme, de celuicy dans le quatrieme, 
du quatrieme dans le cinquieme, et ainsi de suite. Del^ il est clair, 
que dans le passage du premier dans le troisieme sera= r^ : 1 pour les 
rayons rouges, et=i;2: i pour les violets: de meme dans le passage du 
premier dans le quatrieme les raisons seront r^:l eX v^:\. 

Done si dans le passage dans un milieu quelconque la raison de 
refraction des rayons rouges est=r'*:l, celle des rayons violets sera 
=t;":l; tout cela est parfaitement conforme aux principes du grand 
Newton. Posons r»=/?, ett;«=:^ desorte que i2 ;] , et ^: 1 expri- 
ment les raisons de refraction des rayons rouges et violets dans un 
passage quelconque: et ayant nlr=lR etn lv=l Fnousauronsl R: 

lrz=l V-.lvy ou— — =— -. Ou bien mettes t;=r«. et a cause de / v:=. 
I V I V 

I Tt 1 

« / r, on aura— -=^, oulF=:ccl R, et partant F=zR». 



32 Letters relating to a Theorem^ S^c. 

Voila done le fondement du principe, que j'ai employe dans ma 
piece, qui me paroit encore inebranlable: cependant j'en soumets la 
decision a I'illustre Societe Royale, et a votre jugement en particulier, 
ayant I'honneur d'etre avec la plus parfaite consideration, 

MONSIEUR, 

Votre tres humble 

et tr^s obeissant serviteur, 

L, Euler. 

Berlin, 
.Tuin 15, 1752. 



33 



A Description of a Contrivance Jor measuring 
small Angles, hy Mr, John DoUond; commu- 
nicated by Mr, J. Short, F.R S. 

Read May 10, 1753. 

JLiET an object-glass of any convenient focal length (being truly 
ground and well centred) be divided into two equal parts or segments, 
by cutting it straight through the center; and let a piece of machinery 
be so contrived, as to hold these two segments in the same position to 
each other, as they stood in before they were cut asunder; and to be 
capable at the same time of drawing them to different distances from 
that position, in the manner as is represented in the figure. 

Each of these segments will form a distinct image of any object 
to which they are directed; differing in nothing from that, which 
might have been made by the whole glass before it was cut, except in 
brightness. And while these segments are held in their original po- 
sition, the images will coincide, and become one single image as at 
first; but, in proportion as they are drawn off from that situation, the 
images will separate more or less, according to the distance they are 
drawn to. By this means the images of two different objects, or of 
different parts of the same object, not very far from each other, may 

E 



34 A Description of a Contrivance for Measuring small Angles, 

be brought to a contact or coincidence at the focus: and this coinci- 
dence may be viewed to a very great nicety with a proper eye-glass. 

The measure of the angle subtended by the two objects, whose 
images are thus brought to a coincidence, depends upon three things: 
first, a careful observation of the coincidence of the images: — 
secondly, an exact measure of the distance, which the glasses are drawn 
but to from that situation, which makes the image single: — and, 
lastly, a true knowledge of the focal distance of the glass. How the 
angle is to be . found from these measures,, and how it may likewise 
be come at, by viewing two land-objects at a convenient distance, 
will be shewn hereafter in the explanation of the figure. It is easy 
to understand, in the meantime, that the angle will be measured with 
more accuracy, in proportion to the length of the glass, which is used 
for that purpose ; but the difficulty of managing long telescopes is no 
less apparent. Therefore the most practicable method of using this 
micrometer to advantage, is, to apply the divided object-glass to the 
object end of a reflecting telescope: for, as the apertures of these 
sort of telescopes are large in proportion to their lengths, they will 
admit of very long glasses; nor will the measures be any way affected 
by the metals or glasses, which the reflector is composed of: and the 
angles will be found in the same manner, as though the images were 
viewed with a single eye-glass, in the manner of a common refracting 
astronomical telescope; but with this advantage, that, as the images 
will be exhibited larger and distincter by the reflecting telescope; 
and as every part thereof will be much more manageable than a long 
refracting telescope; so the contact or coincidence of the images will 
be more accurately pbserved. 



by Mr. John Dollond, 35 

It would be however unnecessary now, as well as impro- 
per, to say much about the advantages of this method 
above those which have hitherto been put in practice; 
because, as a machine is now' making for this purpose, A H B 
the experiments, which will shortly be tried, will be more 
convincing, as well as more intelligible, than any thing 
that might be offered at present. 

Explanation of the Figure. 

The two semicircles represent the two segments of the 
object-glass, whose centers C and D are drawn off to the 
distance C D, and the points A and B are two objects, or 
different parts of the same object; therefore the lines 
ACG and BDG represent two rays that pass through 
the centres or poles of the segments, and are therefore 
not at all refracted, but go straight through to G, where they 
intersect; and G being the respective focus to the distance 
of the objects from the glass, the two images will coincide 
at that point. It appears from the figure, that ABiCD: : 
GH'. GE; and from a common proportion in optics, GH: 
GE::HE: EF. Therefore, AB.CD-.iHEi EF; F being 
the focus of parallel rays; and consequently the angles 
AEB and CFD are equal. That is, the angle subtended 
by the distance of the centres of the segments from the 
distance of the focus of parallel rays is equal to the angle 
subtended by the distance between the objects A and B 
from the end of the telescope. 

E 2 



3d 



An Explanation of an Instrument Jhr measuring 
small Angles, the Jirst Account of which was 
read before the Royal Society, May 10, 1753. 
Sy Mr, John DoUond. In a Letter to James 
Short, M.A. and F.R.S. 

Read April 25, 1754. 

SIR, 

1 HE account which I gave you, some time ago, of 
a new micrometer, was contained in as few words as possible; being 
rather desirous, that experiments might be made, before I said much 
concerning it: — ^but since your many repeated experiments have con- 
firmed what was expected from it, I have endeavoured to draw up a 
more full account of this instrument, with demonstrations of the 
principles which it is fopnded upon, which I here send you enclosed, 
and which you may lay before the Royal Society, if you think proper. 

I am, SIR, 

Your most obedient, humble servant, 

John DoUond. 

Denmark Court, 
April 4^ 1754. 



37 



Explanation of an Instrument for Measuring Small Angles, S^c. 



JSeFORE I enter upon particulars relating to this micrometer, it 
will be proper to make a few preparatory observations on the nature of 
spherical glasses, so far as may be necessary to render the following 
explanation more easily understood. 

Observation I. — It is a property of all convex spherical glasses to 
refract the rays of light, which are transmitted through them, in such 
a manner, as to collect all those that proceed diverging from any one 
point of a luminous object, to some other point; whose distance from 
the glass depends chiefly on its convexity, and the distance of the 
object from it. 

Observation II. — ^The point, where the rays are thus collected, may 
be considered as the image of that point, from which they diverge. 
For if we conceive several radiant points thus emitting rays, which, 
by the refractive quality of the glass, are made to converge to as many 
other points, it will be an easy matter to understand, how every part 
of the object will be truly represented. As this property of spherical 
glasses is explained and demonstrated by all the writers on optics, it 
being the very foundation of the science^ the bare mention of it is 
sufficient for the present purpose. 

Observation III. — It will be necessary, however, to observe farther, 
that the lines connecting every point in the object, with its corres- 
ponding ones in the image, do all intersect in a certain point Qf the 
axis or line passing through the poles of the glass, wker^e its two 



38 Explanation of an Instrument for Measuring Small Angles, ^c. 

surfaces are parallel, and may be properly called its centre: whence it 
appears, that the angles subtended by the object and its image from 
that point, must be equal: and therefore their diameters will be in the 
same ratio, as their distances from that point. 

Observation IV. — As the formation of the image by the glass depends 
entirely on the property above-mentioned, that is to say, its collecting 
all the light, that is incident on it, from the several points of the 
object into as many other points at its focus ; it follows, that any seg- 
ment of such a glass will also form an image equal, and every way 
similaf, to that exhibited by the whole glass; with this difference only, 
that it will be so much darker, as the area of the segment is less than 
that of the whole glass. 

Observation V. — ^The axis of a spherical glass in a line connecting 
the centres of the spheres, to which the two surfaces are ground; and 
wherever this line passes through the glass, there ^the surfaces are 
■parallel. But if it happens, that this line does not go. through the 
substance of the glass, such a glass is said to have no internal centre; 
but it is conceived to be in its plane produced, till it meets the axis: 
and this imaginary point, though external to the glass, is as truly its 
centre, and is as fixed in its position to it, as if it were actually within 
its substance. 

Observation VI. — If a spherical glass, having its centre or pole near 
its middle or centre of its circumference^ should be divided by a 
straight line through the middle; the centre will be in one of the seg- 
ments only. For how exact. soever a person may be supposed to be 
in cutting it through the centre; yet 'tis hard to conceive, how a ma- 
thematical point should be divided in two: therefore the centre will 



by Mr. John Dollond. 39 

be internal to one of the segments, and external to the other. But 
if a small matter be ground away from the straight edge of each seg- 
ment, both their centres will become external ; and so they will more 
easily be brought to a coincidence. 

Observation VII. — If these two segments should be held together, 
so as to make their centres coincide; the images, which they give of 
any object, will likewise coincide, and become a single one. This 
will be the case, when their straight edges are joined to make the glass, 
as it were, whole again: but let the centres be any-how separated, 
their images will also separate, and each segment give a separate and 
distinct image of any object, to which they may be exposed. 

Observation VIII. — ^Though the centres of the segments may be 
drawn from their coincidence, by removing the segments in any 
direction whatever; yet the most convenient way for this purpose is, 
to slide their straight edges oiie along the other, till they 
are removed, as the figure in the margin represents 
them: for thus they may be moved without suffering 
any false light to come in between them. And by this 
way of removing them, the distance between their cen- 
tres may be very conveniently measured; viz. by having a Vernier's 
division, commonly, though falsely, called a Nonnius's, fixed to the 
brass-work, that holds one segment, so as to slide along a scale on 
the plate, to which the other part of the glass is fitted. 

Observation IX. — As the images of the same object are separated 
by the motion of the segments, so those of different objects, or dif- 
ferent parts of the same object, may be made to coincide. Suppose 
the sun, moon, or any planet, to be the object; the two images 




40 Explanation of an Instrument for Measuring Small Angles , S^c. 

thereof may, by this contrivance, be removed, till their opposite 
edges are in contact: in vvhich case, the distance between the centres 
of the two images will be equal to the diameter of either; and so of 
any other object whatever. 

Observation X. — This divided glass may be used, as a micrometer, 
three different ways. In the first place, it may be fixed at the end of 
a tube, of a suitable length to its focal distance, as an object-glass; 
the other end of the tube having an eye-glass fitted as usual in astro- 
nomical telescopes. Secondly, it may be applied to the end of a tube 
much shorter than its focal distance, by having another convex glass 
within the tube, to shorten the focal distance of that, which is cut 
in two. Lastly, it may be applied to the open end of a reflecting 
telescope; either of the Newtonian, Gregorian, or Cassegrain con- 
struction. And though this last method is much the best, and most 
convenient, of the three; yet, as the first is the most natural, as well 
as tlie easiest to be understood, it will be proper to explain it fully, 
and to demonstrate the principles, on which this micrometer' is con- 
structed, by supposing it made use of in the first way: — which being 
done, the application of it to other methods will be readily under- 
stood. 

, Having thus, by the foregoing observations, given a general idea of 
the nature and effects of this divided object-glass, I shall proceed to 
demonstrate the principles, from whence the measures of the angles 
are to be obtained by this instrument; which will be done by the 
following propositions. 



ly Mr, John Dollond. 



A\ 



PROPOSITION I. 



Suppose a divided object-glass fixed at the end of a tube, j^ JX B 

according to the first method^ and the tube directed to 
the object intended to be measured; and suppose, like- 
wise, the segments removed from their original position, 
in the manner directed under Observation VIII. till the 
opposite edges of the tivo images are seen in contact at 
the focus of the eye-glass: then, I say, the angle sub- 
tended^ by the distance between the centres of the seg- 
ments, from the focus of the eye-glass, where the edges 
are seen in contact, is equal to the angle subtended by 
the diameter of the object from that same point. 



DEMONSTRATION. 

Let the line A B represent the diameter of the object 
to be measured; and the points CD the centres of the 
two glass segments: also G the focus where the images 
of the extremities of the object are coincident. It is 
evident, from Observation III. that AG and B G are 
straight lines, that pass through the centres of the seg- 
ments, and connect the extreme points of the object 
with their corresponding points in the images; and 
therefore, as the diameter of the object and the distance 
between the centres of the segments are both inscribed 
between these two lines, they must needs subtend the 



F 



42 Explanation of an Instrument for Measuring Small Angles, 8^c. 

same angle from the point where those lines meet; which is at G. 
Q. E. D. 

The focal distance C G, or D G, is variable, according to the dis- 
tance of the object from the glass: so that it decreases as the distance 
of the object from the glass increases; and when the object is so far 
off, that the focal length of the glass bears no proportion to its dis- 
tance; then will it be least of all, as C F or D F; and the point 
F is called the focus of parallel rays. Any other focus, as G, being 
the focus of a near object, is called a respective focus; as it respects a 
particular distance: but the focus of parallel rays respects all objects 
that are at a very great distance; such as is that of all the heavenly 
bodies. 

PROPOSITION II. 

The distance H^ of the object from the glass is to E F, the focal dis- 
tance of parallel rays, as the distance H G of the object from its 
image is to E G, the distance of the image from the glass: that is, 
HE : EF :: HG : EG. 

The ' demonstration of this proposition may be gathered from any 
treatise of dioptrics; it being a general rule for finding the respective 
focus to any given distance, when the focus of parallel rays is known. 

PROPOSITION III. 

The angle subtended by the diameter of the object, from the glass, is 
equal to that subtended, by the opening of the centres of the segments, 
from the focus of parallel rays. That is, the angle A E B equal to 
the angle C F D. 



by Mr, John Dollond. 43 

DEMONSTRATION. 

It appears, by inspection of the figure, that ABi CD: :HG : EG. 

And by the last proposition HEiEF: :HG:EG. 

Then, as the two last terms of these two analogies are alike; the 
two first terms of one will be in the same proportion as the two first 
terms of the other; which gives the following proportion: AB: CD: : 
HE : EF. Whence the truth of the proposition is evident. 

From this proposition it appears, that the angle subtended by the 
diameter of the object from the glass, is found without any regard to 
the distance of the object, or to the distance of the respective focus, 
where the image is seen; as the measure depends intirely upon the 
focus of parallel rays and the opening of the segments. We may 
likewise, from hence, derive a rule for the quantity of the angle, 
without considering the length of the glass. Let an object, whose 
diameter is known, be set up at some known distance; the angle it 
will subtend from the glass may then be found by trigonometry: then 
let it be measured by this micrometer, and the distance, between the 
centres of the segments, found on the scale already mentioned, will 
be the constant measure of the same angle, in all other cases: because 
the distance of the object makes no alteration in the measure of the 
angle, as has been demonstrated: and thus having obtained the dis- 
tance between the centres of the segments, which answers to any one 
angle, all other distances may be computed by the rule of three. 

All that has been hitherto said relates to the first method of using 
this micrometer; that is, by fitting it to the end of a tube suited to 
its focal length, and by viewing the images with a proper eye-glass, in 
the manner of an astronomical telescope. But the length of the 

F 2 



44 Explanation of an Instrument Jbr Measuring Small Angles, ^c. 

tube, in this way, would be very troublesome; and therefore it will be 
proper to consider other methods, foran easier management. I shall, 
therefore, proceed to the second method, mentioned in Observation X. 
which is, by using another object glass to shorten the focus of that 
which serves for the micrometer. To facilitate the understanding of 
this method; it will be necessary to premise the following observation. 

Observation XI. — Rays of light, which are brought to such con- 
vergency as to form the image of an object, proceed, after that, 
diverging, in the manner they did when they issued from the object 
before they were transmitted through the glass; and therefore they 
may be again collected by another spherical glass, so as to form a 
second representation of the same object; which may again be repeated 
by a third glass, 8^c. So that the first image may be considered as an 
object to the second glass, and the second image will be an object to 
the third, and so on. Though these images may be very different, 
in respect to their magnitudes, yet they will be all similar; being true 
representations of the same object: this will hold good, though the 
second glass should be put so near the first as to receive the rays be- 
fore the image is formed: for as the rays are tending to meet at a 
certain distance, the second will receive them in that degree of con- 
vergency, and, by an additional refraction, bring them to a nearer 
focus; but the image will still be similar to that which would have been 
made by the first glass, if the second had not been there. 

Upon this principle all refracting telescopes are made; some of 
which are a combination of four, five, or six glasses. The first glass 
forms an image of the object; the second repeats the image, which 
it receives from the first; and so on, till the last glass brings a true 



iy Mr, John I>ollond. ' 45 

representation of the object to the eye. The same may be said of re- 
flecting telescopes: for a spherical mirror acts in the same manner, in 
that respect, as a spherical glass. 

Now let this be applied to the subject in hand. Suppose the focal 
distance of the divided object-glass to be about forty feet; and suppose 
the segments to be opened wide enough to bring the opposite edges 
of an object in contact: then let. another object-glass, uncut, be fixed 
within the tube, of a proper degree of convexity, to shorten the focus 
of the other as much as may be required; suppose to twelve feet: by 
what has been just now observed, this glass will represent the two 
images in the same form which would have been exhibited by the 
divided glass, if this other glass had not been there. For though the 
images are not yet formed, when the second glass receives the rays: 
yet, as those rays are converging towards it, the second glass must 
represent those images in the same position, and form, as the ten- 
dency of the rays requires. For while the segments are fixed in their 
position to each other, their images will also be fixed in their position; 
and let them be repeated ever so many times, by refraction through 
spherical glasses, or by reflection from spherical mirrors, they can 
suffer no alteration in their position to one another. By this means, 
the telescope may be shortened, at pleasure, though the scale for the 
measure of the angles will remain the same. The only inconvenience, 
which the shortness of the telescope introduces, is a want of sufficient 
distinctness; which will so far hinder the exactness of the observation, 
as the contact of the edges cannot be so accurately determined, as 
they might be with longer telescopes. 

This difficulty is intirely removed by fixing the divided glass at the 



4.Q Explanation of an Instrument for Measuring Small Angles , 8^c. 

end of a reflecting telescope: for the reflections and refractions, which 
the rays nmust undergo in passing through the telescope, will no way 
alter the position of the images, which the rays, that have passed 
through the segments, are tending to: for, as has been already ob- 
served, a number of reflections and refractions may repeat the images, 
and alter their magnitudes; but can make no alteration in their 
proportions. 

Therefore this way of fixing the divided glass to a reflecting teles- 
cope, which was the third method proposed, is, by far, the best; as 
such telescopes of moderate and manageable lengths, when well made, 
are capable of magnifying considerably, and shewing objects to great 
advantage. This micrometer being applicable to the reflecting teles- 
cope, with so much certainty, is no inconsiderable advantage: for 
any one will easily understand, that, to measure the diameter of a 
planet exactly, . it is necessary, that the planet be magnified, and 
shown distinctly, which could not be obtained, in the common way, 
without very great lengths; such as rendered it very diflicult, , not to 
say impracticable, to take exact measures. Besides, the common mi- 
crometer is limited, in this respect, upon another account; viz. because 
the diameter of the planet cannot be measured, without having the 
whole planet within the field of the telescope, which confines the mag- 
nifying power within very narrow bounds; whereas, by this method, 
nothing more is required, than to see the contact of the edges, which 
allows the magnifying power to be increased at pleasure. 

In the common micrometer, the object is to be taken between two 
wires, so that the contact of its edges with those wires cannot be 
observed at one view; and the least motion of the telescope, whilst 



hy Mr, John Dollond, Af 

the observer is turning his eye from one wire to the other, must oblige 
him to repeat the observation; whereas, by this method, the contact 
of the edges of the images is not at all affected by the motion of the 
telescope. Whence the comparison of this micrometer with the 
common sort, in this respect, stands thus: the one requires great 
steadiness in the telescope, but yet it is applicable to none, but such 
as are very difficult to keep steady; the other does not require such 
steadiness, though it is applicable to short telescopes, which are easily 
managed, v . 

These advantages not only add to the certainty of the observation, 
but assist vastly in the expedition ; for an observer may make twenty > 
observations, in this way, where he could scarcely, with much 'fatigue, 
be sure of one with the common micrometer. Expedition in making 
observations, must be allowed a very great advantage, in this climate, 
where the uncertainty of the weather renders astronomical observations 
so precarious, that no opportunities, even the most transient, should 
be let slip. An instance of this was given to the Royal Society, in an 
account of the eclipse of the sun last October. 

As the motion of the telescope gives the observer no great incon- 
venience, in this method; neither does the motion of the object at all 
disturb his observation (I mean such a motion, as that of the heavens 
is.) This gives him leave to take the diameter of a planet, in any 
direction; or the distance between two stars or planets, let their 
situation be how it will ; in which respect the common micrometer is 
absolutely defective; as it can give no angles, but such as are per- 
pendicular to the line of their motion ; though the diameters of the 
planets, in other directions, are very much wanted; it being highly 



48 Explanation of an Instrument for Measuring Small Angles, S^c. 

probable, from the laws of motion, and what we see in Jupiter, that 
such planets, as revolve round their axes, have their polar diameters 
shorter than their equatorial ones. 

The distances of Jupiter's satellites from one another, or from Ju- 
piter's body, cannot be measured, with any certainty, in the common 
way, as their position is always very far from being at right angles 
with the line of their motion: neither can the moon's diameter, which 
must be taken from horn to horn, scarce ever be obtained that way, 
because it very rarely happens, that the diameter, to be measured, lies 
at right angles to the line of her motion. The same may be said of 
the distance between two stars. But this micrometer gives angles, in 
every direction, with equal ease and certainty; the observation being 
also finished in an instant, without any trouble or fatigue to the ob- 
server. For as there are no wires made use of, this way, in the field 
of the telescope, so the observer has no concern about any illumination. 
The largeness of the scale deserves also to be taken notice of, as it 
may, in this micrometer, be increased almost at pleasure, according 
as the smallness of the object requires. Another inconvenience 
attending the common micrometer is, the variation of the scale, ac- 
cording to the distance of the object. As the telescope must be 
lengthened, or drawn out farther, for short distances; the scale, which 
depends upon that length, is thereby increased; which renders the 
measure of the angle very undertain: whereas, in this micrometer, the 
scale is the same at all distances; so that the angle may be measured 
with the utmost certainty, without any regard to the distance of the 
object. 



hy Mr. John Dollond. 49 

, Upon the whole, it may be concluded, that this micrometer is a 
complete instrument in its kind; having many advantages above the 
common sort, without any of their disadvantages: and there is no 
doubt, but, when brought into practice, it will tend much to >the 
advancement of astronomy. 



G 



50 



An Account of some Experiments concerning the 
different Refrangibility of Lighit. By Mr. John 
DoUond. With a Letter Jrom James Short, 
M.A, F.R.S. Acad. Reg. Suec. Soc. 

To the Rev. Dr. Birch, Secret. R. S. 
Read June 8, 1758. 

DEAR SIR, 

X HAVE received the enclosed paper from Mr. 
Dollond, which he desires may be laid before the Royal Society. It 
contains the theory of correcting the errors arising from the different 
refrangibility of the rays of light in the object-glasses of refracting 
telescopes; and I have found, upon examination, that telescopes made 
according to this theory are intirely free from colours, and are as dis- 
tinct as reflecting telescopes. 

I am, DEAR SIR, 

Your most obedient humble servant, 

James Short. 

Surrey Street, 

June 8, 1758. ' ' 



51 



Experiments concerning the different Refrangihility of Light, 8^c. 



XT is well known, that a ray of light, refracted by passing through 
mediums of different densities, is at the same time proportionally 
divided or spread into a number of parts, commonly called homogeneal 
rays, each of a different colour; and that these, after refraction, pro- 
ceed diverging; a proof, that they are differently refracted, and that 
light consists of parts that differ in degrees of refrangibility. 

Every ray of light passing from a rarer into a denser medium, is 
refracted towards the perpendicular; but from a denser into a rarer 
one, from the perpendicular; and the sines of the angles of incidence 
and refraction are in a given ratio. But light consisting of parts, which 
are differently refrangible, each part of an original or compound ray 
has a ratio peculiar to itself; and therefore the more a heterogeneous 
ray is refracted, the more will the colours diverge, since the ratios of 
the sines of the homogeneal rays, are constant; and equal refractions 
produce equal divergencies. 

That this is the case when light is refracted 'by one given medium 
only, as suppose any particular sort of glass, is out of all dispute, being 
indeed self-evident; but that the divergency of the colours will be the 
same under equal refractions, whatsoever mediums the light may be 
refracted by, though generally supposed, does not appear quite so 
clearly. 

However, as no medium is known, which will refract light without 
diverging the colours, and as difference of refrangibility seems thence 

G 2 



52 Experiments concerning the different RefrangiUlity of Light, 

to be a property inherent in light itself, opticians have, upon that 
consideration, concluded, that equal refractions must produce equal 
divergencies in every sort of medium: whence it should also follow, 
that equal and contrary refractions must not only destroy each other, 
but that the divergency of the colours from one refraction would 
likewise be corrected by the other; and there could be no possibility 
of producing any such thing as refraction, which would not be affected 
by the different refrangibility of light; or, in other words, that how- 
ever a ray of light might be refracted backwards and forwards by 
different mediums, as water, glass, 8^c. provided it was so done, that 
the emergent ray should be parallel to the incident one, it would ever 
aft6r be white; and conversely, if it should come out inclined to the 
incident, it would diverge, and ever after be coloured. From whence 
it was natural to infer, that all spherical object-glasses of telescopes 
must be equally affected by the different refrangibility of light, in 
proportion to their apertures, whatever material they may be formed 
of. 

But it seems worthy of consideration, that notwithstanding this 
notion has been generally adopted as an incontestable truth, yet it 
does not seem to have been hitherto so confirmed by evident experi- 
ments, as the nature of so important a matter justly demands; and 
this it was that determined me to attempt putting the thing to issue 
by the following experiment. 

I cemented together two plates of parallel glass at their edges, so 
as to form a prismatic or wedge-like vessel, when stopped at the ends 
or bases ; and its edge being turned downwards, I placed therein a 
glass prism with one of its edges upwards, and filled up the vacancy 



hy Mr. John Bollond, 53 

with clear water: thus the refraction of the prism was contrived to be 
contrary to that of the water, so that a ray of light transmitted 
through both these refracting mediums would be refracted by the 
difference only between the two refractions. Wherefore, as I found 
the water to refract more or less than the glass prism, I diminished 
or increased the angle between the glass plates, till I found the two 
contrary refractions to be equal ; which I discovered by viewing an 
object through this double prism; which, when it appeared neither 
raised nor depressed, I was satisfied, that the refractions were equal, 
and that the emergent rays were parallel to the incident. 

Now, according to the prevailing opinion, the object should have 
appeared through this double prism quite of its natural colour ; for if 
the difference of refrangibility had been equal in the two equal re^ 
fractions, they would have rectified each other : but the experiment 
fully proved the fallacy of this received opinion, by showing the di- 
vergency of the light by the prism to be almost double of that by the 
water; for the object, though not at all refracted, was yet as much 
infected with prismatic colours, as if it had been seen through a glass 
wedge only, whose refracting angle was near 30 degrees. 

N,B. This experiment will be readily perceived to be the same as 
that which Sir Isaac Newton mentions* : but how it comes to 
differ so very remarkably in the result, I shall not take upon me 
to account for J but will only add, that I used all possible pre- 



* Book I. Part ii. Prop. 3. Experiment viii. of his*"Optics. 



54 Experiments concerning the different Refrangihility of Light, 

■ caution and care in the process, and that I keep the apparatus by 
nie to evince the truth of what I write, whenever I may be pro- 
perly required so to do. 

I plainly saw then, that if the refracting angle of the water-vessel 
: could have admitted of a sufficient increase, the divergency of the 
coloured rays would have been greatly diminished, or entirely recti- 
fied ; and there would have been a very great refraction without colour, 
as now I had a great discolouring without refraction : but the incon- 
veniency of so large an angle, as that of the vessel must have been, 
to bring the light to an equal divergency yvith that of the glass prism, 
whose angle was about 6o degrees, made it necessary to try some ex- 
periments of the same kind, by smaller angles. 

I ground a wedge of common plate glass to an angle of somewhat 
less than 9 degrees, which refracted the mean rays about 5 degrees. 
I then made a wedge-like vessel, as in the former experiment, and 
filling it with water, managed it so, that it refracted equally with the 
glass wedge ; or, in other words, the difference of their refractjons 
was nothing, and objects viewed through them appeared neither 
raised nor depressed. This was done with an intent to observe the 
same thing over again in these small angles, which I had seen in the 
prism : and it appeared indeed the same in proportion, or as near as 
I could judge; for notwithstanding the refractions were here also 
equal, yet the divergency of the colours by the glass was vastly 
greater than that by the water ; for objects seen by these two refrac- 
tions were very much discoloured. Now this was a demonstration, 
that the divergency of the light, by the different refrangibility, w^s 



hy Mr. John Dollond, ' 55 

far from being equal in these two refractions. I also saw, from the 
position of the colours, that the excess of divergency was in the 
glass ; so that I increased the angle of the water-wedge, by different 
trials, till the divergency of the light by the water was equal to that 
by the glass ; that is, till the object, though considerably refracted^ 
by the excess of the refraction of the. water, appeared nevertheless 
quite free from any colours proceeding from the different refrangibility 
of light ; and, as near as I could then measure, the refraction by the 
water was about -f of that by the glass. Indeed I was not very exact 
in taking the measures, because my business was not at that time about 
the proportions, so much as to show, that the divergency of the 
colours, by different substances, was by no means in proportion to the 
refractions ; and that there was a possibility of refraction without any 
divergency of the light at all. 

Having, about the beginning of the year 1757, tried these experi- 
ments, I soon after set about grinding telescopic object-glasses upon 
the new principles of refractions^ which I had gathered from them ; 
which object-glasses were compounded of two spherical glasses with 
water between them. These glasses I had the satisfaction to find, as 
I had expected, free from the errors arising from the different refran- 
gibility of light: for the refractions, by which the rays were brought 
to a focus, were everywhere the differences between two contrary re- 
fractions, in the same manner, and in the same proportions, as in the 
experiment with the wedges. 

However, the images formed at the foci of these object-glasses were 
still very far from being so distinct as might have been expected from 
the removal of wso great a disturbance ; and yet it- was not very diffi- 



56 Experiments concerning the different Refrangihility of Light, 

cult to guess at the reason, when I considered, that the radii of the 
spherical surfaces of those glasses were required to be so short, in 
order to make the refractions in the required proportions, that they 
must produce aberrations, or errors, in the image, as great, or 
greater, than those from the different refrangibility of light. And 
therefore, seeing no method of getting over that difficulty, I gave 
up all hopes of succeeding in that way. 

And yet, as these experiments clearly proved, that different sub- 
stances diverged the light very differently, in proportion to the refrac- 
tion ; I began to suspect, that such a variety might possibly be found in 
different sorts of glass, especially as experience had already shown, 
that some made much better object-glasses, in the usual way, than 
others : and as no satisfactory cause had as yet been assigned for such 
difference, there was great reason to presume, that it might be owing 
to the different divergency of the light by their refractions. 

Wherefore, the next business to be undertaken, was to grind 
wedges of different kinds of glass, and apply them together, so that 
the refractions might be made in contrary directions, in order to dis- 
cover, as in the foregoing experiments, whether the refraction and di- 
vergency of the colours would vanish together. But a considerable 
time elapsed before I could set about that work; for though I was de- 
termined to try it at my leisure, for satisfying my own curiosity, yet I 
did not expect to meet with a difference sufficient to give room for 
any great improvement of telescopes ; so that it was not till the latter 
end of the year that I undertook it, when my first trials convinced 
me, that this business really deserved my utmost attention and appli- 
cation. 



by Mr. John Dollond. 57 

I discovered a difference, far beyond my hopes, in the refractive 
qualities of different kinds of glass, with respect to their divergency 
of colours. The yellow or straw-coloured foreign sort, commonly 
called Venice glass, and the English crown glass, are very nearly alike 
in that respect, - though in general the crown glass seems to diverge 
the light rather the least of the two. The common plate glass made 
in England diverges more ; and the white crystal or flint English glass, 
asi it is called, most of all. 

It was not now my business to examine into the particular qualities 
of every kind of glass that I could come at, much less to amuse my- 
self with conjectures about the cause, but to fix upon such two sorts 
whose difference was the greatest; which I soon found to be the 
crown, and the white fiint or crystal. I therefore ground a wedge of 
white flint of about 25 degrees, iand another of crown of about 29 de- 
grees, which refracted nearly alike ; but their divergency of the co- 
lours was very different. I then ground several others of crown to 
different angles, till I got one, which was equal, with respect to the 
divergency oi the light, to that in the white flint : for when they 
were put together, so as to refract in contrary directions, the re- 
fracted light was intirely free from colour. Then measuring the re- 
fractions of each wedge, I found that of the white glass to be to that 
of the crown nearly as 2 to 3 ; and this proportion would hold very 
nearly in all small angles. Wherefore any two wedges made in this 
proportion, and applied together, so as to refract in a contrary di- 
rection, would refract the light without any difference of refrangi- 
bility. ■ ^ 

H 



58. Experiments concerning the different Refrangihility of Light, 

To make therefore two spherical glasses, that shall refract the 
light in contrary directions, it is easy to understand, that one must 
be concave, and the other convex ; and as the rays are to converge 
to a real focus, the excess of refraction must evidently be in the con- 
vex ; and as the convex is to refract most, it appears from the experi- 
ment, that it must be made with crown glass, and the concave with 
white flint or]ass. 

And further, as the refractions of spherical glasses are in an 
inverse ratio of their focal distances ; it follows, that the focal dis- 
tances of the two glasses should be inversely as the ratios of the 
refractions of the wedges : for being thus proportioned, every ray of 
light that passes through this combined glass, at whatever distance 
it may pass from its axis, will constantly be refracted, by the dif- 
ference between two contrary refractions, in the proportion required ; 
, and therefore the different refrangihility of the light will be intirely 
removed. 

Having thus got rid of the principal cause of the imperfection 
of refracting telescopes, there seemed to be nothing more to do, 
but to go to work upon this principle : but I had not made many 
attempts, before I found, that the removal of one impediment had 
introduced another equally detrimental (the same as I had before 
found in two glasses with water between them) : for the two glasses, 
that were to be combined together, were the segments of very 
deep spheres ; and therefore the aberrations from the spherical sur- 
faces became very considerable, and greatly disturbed the distinctness, 
of the image. Though this appeared at first a very great difficulty, 
yet I was not long without hopes of a remedy : for considering 



by Mr, John Dollond, 59 

the surfaces of spherical glasses admit of great variations, though 
the focal distance be limited, and that by these variations their 
aberrations may be made more or less, almost at pleasure, I plainly 
saw the possibility of making the aberrations of any two glasses 
equal ; and as in this case the refractions of the two glasses were 
contrary to each other, their aberrations, being equal, would intirely 
vanish. 

And thus, at last, I obtained a perfect theory for making object- 
glasses, to the apertures of which I could scarcely conceive any limits : 
for if the practice could come up to the theory, they must certainly 
admit of very extensive ones, and of course bear very great magni- 
fying powers. 

But the difficulties attending the practice are very considerable. 
In the first place, the focal distances, as well as the particular surfaces, 
must be very nicely proportioned to the densities or tefracting powers 
of the glasses ; which are very apt to vary in the same sort of glass 
made at different times. Secondly, the centres of the two glasses 
must be placed truly on the common axis of the telescope, other- 
wise the desired effect will be in a great measure destroyed. Add to 
these, that there are four surfaces to be wrought perfectly spherical ; 
and any person, but moderately practised in optical operations, 
will allow, that there must be the greatest accuracy throughout the 
whole work. 

Notwithstanding so many difficulties, as I have enumerated, I have, 
after numerous trials, and a resolute perseverance, brought the matter 
at last to such an issue, that I can construct refracting telescopes, with 

H 2 



6o Experiments concerning the different Refrangihility, 8§c. 

such apertures and magnifying powers, under limited lengths, as, in 
the opinion of the best and undeniable judges, who have expe- 
rienced them, far exceed any thing that has been hitherto produced, 
as representing objects with great distinctness, and in their true 
colours. 

John Dollond. 



^^P' 



■% 







m 



* <.# 




%» 



/^ //'/rnv/;/ //V ./ '/'//r'///AW// /l-n/// /t/i nr/z/i/i 11/ J'lr/'/i/i/iif fir J.//,'/i/u/ir /i.. I. 



6i 



Some Account of the JDiscovay, made hy the late 
3Ir, John Dollond, F.R S. which led to the 
grmul Improvem^ent of Refracting Telescopes, 
in Order to correct some Misrepresentations, in 
Foreign Publications, of that Discovery : with 
an Attenvpt to account for the Mistake in an 
Experiment made hy Sir Isaac Newton; on 
which Exp)erhnent, the Improvejnent of the Re- 
fracting Telescope intirely dejyended. By Peter 
Dollond, Member of the American Philosophi- 
cal Society at Philadelphia. 



ADVERTISEMENT, 

IVlY intention in writing the following paper was, to correct several 
false representations, relating to the invention of the achromatic 
refracting telescope, and to secure to my late father, Mr. John 
Dollond, as well as to this country, the honour of so valuable a dis- 
covery. 



62 Advertisement hy Mr. Peter Dollond, 

With this view, the paper was presented to the Royal Society, by 
the Rev. Dr. Maskelyne, Astronomer Royal, in expectation of its 
being published in the Philosophical Transactions, It was read at a 
meeting of the Society on the 21st of May, 1789; but afterwards, 
contrary to my expectation, it was resolved, in a council of the So- 
ciety, that the paper should not be printed in their Transactions; I 
therefore take this method of submitting it to the public; as I hum- 
bly conceive, it relates to a subject of a sufficient degree of importance 
to claim their attention. 



Peter DoUond, 



St, Paul's Church-yard, 
Sept. 1, 1789. 



63 



Some Account of the Improvement in Rejracting Telescopes, $s^. 



The correction of any inaccuracies or false representations in the 
history of science is certainly of some consequence to the public, and 
deserves the attention of the Royal Society ; particularly so, when 
such false representation tends to deprive any one of that praise, to 
which he may be justly entitled, by having contributed tdwards the 
advancement of science ; even though it may be in things of little 
moment. Then certainly it must be much more so, when it relates 
to matters of great importance ; such as was the discovery which 
brought forward the grand improvement of the refracting telescope. 

I was led to these reflections, by having seen some accounts of that 
discovery in different publications, which were related in a manner 
that lessened the merit of my late father John Dollond, and gave it 
to others, who never thought themselves in any manner entitled to 
claim with him, or ever appeared to be inclined so to do. Their own 
characters ^yere too exalted in science to need any additional merit of 
any discovery, to which they had not an undoubted right. 

The celebrated M. Euler, of Berlin, and M. Klinginstierna, pro- 
fessor of mathematics at Upsal, in Sweden, are the persons alluded 
to. These gentlemen have been mentioned by different foreign 
authors, who have had occasion to give accounts of the improve- 
ment of the refracting telescope, as being the discoverers of the 
PRINCIPLE on which that improvement was founded ; and nothing 
has been left to Dollond, but the credit of being the first who put the . 



64 Some Account of the Discovery made by Mr. John Dollond, 

same into practice ; whereby he has been deprived of the honour 
which is justly due to his memory, for having made so useful a dis- 
covery. 

In order to set this matter in a proper light, I shall mention so 
much from Sir Isaac Newton's Optics, as is necessary for the purpose ; 
and then endeavour to prove, that what was attempted by Euler and 
Klinginstiema was not done from any knowledge of the principle on 
which the improvement was founded ; but that Dollond was actually 
the discoverer of that principle, as well as the person who first put the 
same in practice- 
When Newton had made his great discovery of the different re- 
frangibility of light, he fully explained that to be the cause of the 
imperfection of refracting telescopes, and that it was not occasioned 
by the spherical figures of the glasses, as has been the generally 
received opinion. But as mathematicians had made many attempts to 
correct the errors arising from spherical figures, by giving the glasses 
figures from the conic sections, he took that opportunity of mention- 
ing an ingenious thought of his own, of composing the object-glasses 
of two glasses with water between them ; by which means he says, 
that the spherical figures of the glasses might have been corrected, 
and telescopes brought to a sufficient perfection, had it not been for 
the different refrangibility of the several sorts of rays. — Neivtoris Op- 
tics, 3d. Edition, p. QO. 

Newton having completed the principal experiments relating to the 
different refrangibility of light, and having determined the proportions 
of the sines of incidence to the sines of refractions in the different 
coloured rays, as given by his glass prisms, proceeds to try the eighth 



relating to Refracting Telescopes. 65 

experiment of the second part of the first book of his Optics, to dis- 
cover their proportions in different refracting mediums. This expe- 
riment he tried, by placing a prism of glass in a prismatic vessel of 
water. Refracting the light through these different mediums, he 
found that light, as often as by contrary refractions it is so corrected 
that it emergeth in lines parallel to those in which it was incident, 
continues ever afterto be white* but if the emergent rays be inclined 
to the incident, the light will become coloured. — Newton s Optics^ 
p. 112. 

The conclusion drawn from this experiment was, that the di- 
vergency of the different coloured rays was constantly in a given 
proportion to the mean refraction in all sorts of refracting mediums. 
This was the principle established by the Newtonian experiment, and 
was doubted by no one, until the beginning of the year 1757; when 
Dollond tried the same experiment as above related, and found the 
result to be very different; for the light after being refracted in con- 
trary directions through the glass and water prisms, if the emergent 
rays were parallel to the incident rays, they were found to be con- 
siderably coloured ; from whence it followed, that the dissipation of 
the different coloured rays was not in the same proportion to the mean 
refraction in water as in glass. And further experiments proved, that 
there was also a very considerable difference of the same nature to be 
found in different kinds of glass. — See this appendix, p. 50. 

This was the new principle, which brought forward the improve- 
ment of refracting telescopes; a principle so contrary to the 
generally received opinion, that Euler had much difficulty to prevail 
on himself to believe what was told him by his friends on that subject; 



66 Some Account of the Discovery made hy Mr. John Dollond, 

as appears by his own papers published in the Memoirs of the Royal 
Academy at Berlin. For he first supposes the goodness of Dollond's 
telescopes to be owing to the greenish colour of the crown-glass, 
which did not transmit all the red rays; he afterwards endeavours to 
account for it from the construction of the eye-glasses; and at last 
declares it to be very extraordinary, that the English optician should 
have made such an improvement, by reasoning, as it were, in a man- 
ner quite contrary to the nature of things ; for so indeed the new 
discovered principle appeared to him. Notwithstanding these decla- 
rations of Euler, which were published in the year 17^^ M. De la 
Lande, in the second volume of his Astronomy, p. 837, published 
in the year 17^4, says, that Euler, in 1747, endeavoured to correct 
the different refrangibility of light, by a method which Newton 
pointed out for correcting the errors of the spherical figures of the 
glasses; which was, by two lenses with water between them, as re- 
cited above: and he says, that DoUond tried to confute Euler, who 
had demonstrated an error in Newton's theory of colours; but the 
dispute having given occasion to Dollond to examine the thing more 
narrowly, he afterwards acknowledged the error of Newton, and in 
the year 1759 he found out a method of making achromatic telescopes 
that succeeded very well. 

Now this account of De la Lande's is by no means the true state 
of the facts, as appears by the Letters which passed between Euler 
and Dollond, see the former part of this Appendix, pp. 21 — 32 j for 
though Euler argues from his hypothesis, that the result of Newton! s 
experiment could not be exactly as he relates it, yet he does not pre- 
tend to controvert any of Newton's laws of refraction, as being con- 



^ relating to Refracting Telescopes. Qy 

trary to experiment, but believed, that the divergency of the different 
coloured rays differed scarce sensibly from bearing a given proportion 
to the mean refraction, in all sorts of refracting mediums; by which 
it appears, that the error afterwards discovered by Dollond was not 
even suspected by Euler; therefore that part of De la Lande's account 
cannot be true; for Dollond could not be said to acknowledge an error, 
supposed to be discovered by Euler in Newton's theory of coteurs, 
by having actually discovered one himself of a different nature. The 
true state of the fact is, that in 1747 Euler endeavoured to correct 
the errors arising from the different refrangibility of light in object- 
glasses, by a method which was not founded on any experiment, 
but on an hypothesis, which did not appear to be on a true principle, 
so that the attempts which were made to put this method in practice 
did not succeed : this was certainly the case; for after M. Clairaut 
had examined the controversy between Euler and Dollond, he pro- 
nounced, that what Euler had done appeared to be more ingenious 
than useful. 

Euler indeed says, that the structure of the eye gave him the 
greatest reason to suppose, that the different refrangibility might 
be corrected by several refractions through different kinds of mediums; 
for which purpose he thought the eye to be so constructed. But 
this reasoning had no weight with Dollond, as he perceived and 
mentioned to his friends, that the refractions of the eye, at the several 
surfaces and humours, are all made the same way, and consequently, 
for want of contrary refractions, the colours produced by the first 
refractions could not be taken away. How this can subsist with the 
perfection of our vision, has been ingeniously explained by the 

I 2 



68 Some Account of the Discovery made hy Mr. John Dollond, 

Astronomer Royal, in an account which he proposes to lay before the 
Society. — See p. 78 of this Appendix. 

Klinginstierna has likewise been considered as a party concerned 
in the improvement of the refracting telescope ; though De la Lande 
does not mention his name, yet some others do. This has been oc- 
casioned by his having, in the year 1755, considered the controversy 
between Euler and Dollond, and having formed a theorem of his own, 
by which he was also induced to believe, that the result of Newton*s 
experiment could not be as he had related it ; except when the angles 
of the refracting mediums were small. This he communicated to 
Dollond, in a letter to his friend Mr. Mallet, who was then in 
England. As this theorem has never been published in English, I shall 
give a copy of it here, as taken by my father from Klinginstierna's 
letter to Mallet, that mathematicians may judge of the truth of the 
deductions. 

" Remarks on the Law of Refraction of Rays of Light of different 
Kinds, through different Mediums. See Newton's Optics., Book I. Part 
ii. Prop. 3. Eocper. viii. 




relating to Refracting Telescopes. 6g 

" Upon any right line, as TH, let there be drawn two arches TIH, 
TGH, and let a right line TIG be drawn intersecting the arches 
in I and G. Join IH and GH ; let F E K be a transparent wedge, 
having its acute angle FEK equal to the angle IHG; let the two 
faces of this wedge be contiguous to two different transparent me- 
diums ; and let the ratio of refraction out of the medium, that 
joins the surface EF into the wedge, be as the ratio of TH to TI, 
and the ratio of refraction out of the wedge into the medium join- 
ing the surface EK as the ratio of TG to TH. 

" Now if AB represents a ray of light entering into the wedge, 
and the angle AB a is made equal to HIG, then will the angle CB 
a be equal to the angle THI. Ang. BC Z'=ang. THG and DC />== 
HGL; so that the incident ray AB will be parallel to the emergent 
ray CD, which has been twice refracted. 

" Now if the incident ray is compounded of divers simple rays, 
each of which, after two refractions, should emerge parallel to the 
common incident ray, the refractions of each will be represented by 
so many right lines Tig- joining Hf, H^, the same as before. 

" According to Newton's law of refraction quoted above TH— TI 
should be in a constant ratio to TH— TG; that is, if an arch of a 
circle is described on the centre T with the interval T H, meeting 
the lines TIG, Tig in L and /; then by that supposition LI should 
be to LG as li to Ig. But these proportions will not hold, unless L 
and / were in an arch described on the chord TH, but they are in an 
arch whose centre is T. 

" Therefore Newton's law of refraction does not seem to follow 



70 Some Account of the Discovery made bij Mr. John Dollond, 

clearly from his 8th experiment, which our wedge with two conti- 
guous mediums refers to. 

" If we should suppose such a law of refraction as we find necessary 
to bring out every simple ray parallel to the incident, after two re- 
fractions through this wedge FEK, it can be demonstrated, that the 
same law will not have the same effect in another wedge of a different 
angle, but for every different angle there will be a different law re- 
quired. 

" Whence it seems to follow, that there must be some mistake in 
this experiment of Newton's, which he himself gives as an universal 
one, for it does not seem likely that the law which really obtains in 
nature should depend upon a greater or less angle of a wedge. 

" Nevertheless it must be observed, that the less the refractions are, 
the nigher will the Newtonian law be to that which is required for 
producing a perfect parallellism of the emergent rays to the common 
incident ray ; for in this case Llto LG will be very nearly in a given 
ratio. It does not seem that the aberration of the rays in object- 
glasses, proceeding from the different refrangibility, can be corrected 
by any refractions, which is what Mr. Newton plainly insists upon. 
However, this whole affair deserves to be more accurately examined 
by experiments." 

I shall here only remark, that it appears by this copy of a, letter 
from Klinginstierna, that the supposed error in the result of Newton's 
experiment, which he thus labours to demonstrate, is the same as 
before attempted to be ascertained by Euler, and not the error 
which was afterwards discovered by Dollond. 



relating to Refracting Telescopes, 71 

The account given by De la Lande, of the improvement of the re- 
fracting telescope, was copied by most foreign writers on the subject, 
with little variation, except in giving sometimes a little more of the 
honour to Euler, and also making mention of Klinginstierna. 

But in the Eulogy on l^uler, written and published by M. N. Fuss, 
professor of mathematics at St. Petersburg, in the year 1783, p. 41 
and 42, he gives the whole of the discovery to Euler, except " that 
Dollond is allowed to have found out two sorts of glass, which 
crowned at last, in 1757? the happy conjecture of Euler, by the in- 
vention of achromatic telescopes, which formed a new epoch in 
astronomy and dioptrics." As this account is the most curious of any 
I have found, I shall here give it at length, and contrast it with what 
Euler says himself on the subject, in a paper read before the Royal 
Academy of Sciences at Berlin, in 17 64, and published in the 
volume of their Memoirs for 17 66, p. II9. 

Mr. Fuss says, '^ The examination of the Newtonian theory had 
given Euler an opportunity of investigating the different refrangibility 
of light, and the bad effects which the dispersion of the colours pro- 
duced in refracting telescopes, which had been almost intirely aban- 
doned upon account of this defect. The consideration of the 
wonderful structure of the eye made him suppose, that a certain 
combination of different transparent bodies could remedy this* incon- 
venience. He proposed for this purpose, in the year 1747, object- 
glasses composed of two glasses, the cavity between which could he 
filled with water. 

" His opinion was attacked by the famous English artist, Dollond, 
who opposed to him the authority of Newton: M. Euler soon shewed 



ft Some Account of the Discovery made by Mr, John DoUond, 

h'ltn the error of his principles. Some experiments made upon me- 
aiiSGuses, the cavities of which were filled with different liquids, con- 
firmed him in his opinion: and Mr. Dollond, who had in the mean 
time discovered two sorts o£ glass, which were proper for examining 
it further, crowned at last, in 1757, the happy Oonjecture of M. 
Euler, by the invention of achromatic telescopes, which formed an 
epoch in astronomy and dioptrics. 

" The success of Mr. Dollond, who availed himself, with so much 
advantage, of a discovery, which he had at first attacked as contrary 
to experiment, induced M. Euler to extend his researches further 
upon the subject of dioptric instruments, &c." 

I shall now subjoin a translation of M. Euler's paper, read at the 
Academy of Sciences at Berlin in the year 1764. 

*' Although I have already frequently discussed this subject^ I see 
myself again obliged to resume it, in consequence of the astonishing 
discoveries which have been lately made upon the nature of glass, and 
its different kinds. I am not ashamed frankly to avow, that the first 
accounts, which were published of it, appeared so suspicious, and 
even so contrary to the best established principles, that I could not 
prevail upon myself to give credit to them. That there should be two 
kinds of glass, in which the refraction of the mean rays is nearly 
equal, whilst that of the extremes differs most enormously, appeared 
to me to shock good sense; and perhaps I should never have submitted 
to the proofs, which Mr. Dollond produced to support this strange 
phenomenon, if Mr. Clairaut, who must at first have been equally 
surprized at it, had not most positively assured me, that Dollond's 
experiments were but too well founded. But at length the experi- 



relating to Refracting Telescopes, 73 

ments made at Petersburg by M. Zeiher have efFectually succeeded ia 
removing my prejudice; that ingenious philosopher having incontesta- 
bly proved that it is the lead;, which is used in some compositions of 
glass, that produces in it that strange quality of augmenting the dis- 
persion of the extreme rays, without changing sensibly the refraction 
of the mean ; and by increasing the quantity of lead in the composi- 
tion of glass, he has been enabled to make glass, which produces a 
much greater dispersion of the rays than the flint-glass of Dollond. 

" Now I must intirely renounce this principle, whidi until now 
has appeared so well-founded, that the dispersion of the extreme rays 
depends solely upon the refraction of the mean rays ; and I am obli- 
ged to acknowledge, that the dispersion depends principally upon the 
quality of the glass, without the mean refraction thereof being sensi- 
bly affected thereby." 

As it appears by the above paper, that Euler was at last so con- 
vinced of the truth of the discovery made by Dollond, as to renounce 
his favourite hypothesis, it must be inferred, that the account given 
of this matter by Fuss is very far from being the true state of the 
facts, and indeed so much so, as to be very inexcusable, even in an 
eulogy. 

There is another publication of a later date, which I shall take the 
liberty of mentioning, " Extracts of the Observations made at the 
Royal Observatory at Paris, in the year l^JQ^ > by Count Cassiniy In 
page 106 he gives an account of the improvement of the refracting 
telescope, by way of prelude to his describing a method proposed by 
M. I'Abbe Rochon, of putting fluids, and also a kind of mastic, be- 
tween the glasses of achromatic object-glasses, as a good method of 

K 



74 Some Account of the Discovery, made by Mr, John Dollondj 

mending bad glasses, or, as he calls it, a method to correct 
the non-sphericity of the glasses ; which he mention^ as being similar 
to that ingenious idea proposed by Newton, for correcting the errors 
of the sphqrical figures of object-glasses. The account he gives of 
the improvement of the refracting telescope is as follows. He says, 
" It was the celebrated Euler who first proposed to correct the errors 
arising from the different refrangibility, by using different refracting 
mediums, s'- h as water and glass. The late Mr. Dollond having 
availed himself of and realized this ingenious idea, has a just right to 
partake of the glory." — By these publications it seems, that Dollond, 
who explained the fallacy of Euler's hypothesis, who afterwards dis- 
covered the true principle, on which the different refrangibility of 
light could be corrected, and he, who put the same in practice, so 
much to the benefit of science, is only to be allowed to partake of 
the glory, and that with Euler, who never himself thought he had 
the least right to claim any part of the discovery with Dollond, as 
most fully appears by the paper above recited from the Berlin 
Memoirs. 

I can account for these false representations no other way than by 
supposing, that those who wrote them have not taken sufficient pains 
to inform themselves of the true history of the discovery; for I 
would not wish to attribute what they have said to any partiality ; and 
I am induced to hope, that when the state of facts which I have here 
adduced shall be candidly considered, that they will retract their de- 
clarations, and acknowledge, that Dollond was the sole discoverer of 
the principle which led to the improvement of refracting telescopes. 

I now come to a more agreeable part of this paper, which is, to 
endeavour to reconcile the different results of the 8th experiment of 



relating to Refracting Telescopes » 75 

the second part of the 1st Book of Newton's Optics^ as related by 
himself, and as it was found by Dollond, when he tried the same 
experiment, in the year 1757. Newton says, that light, as often as 
by contrary refractions it is so corrected, that it emergeth in lines 
parallel to the incident, continues ever after to be white. Now DoUond 
says when he tried the same experiment, and made the mean refracti- 
on of the water equal to that of the glass prison, so that the light 
emerged in lines parallel to the incident, he foi..^J the divergency of 
the light by the glass prism to be nearly double to what it was by the 
water prism. The light appeared to be so evidently coloured, that it 
was directly said by some persons, that if Newton had actually tried 
the experiment, he must have perceived it to have been so. Yet who 
could for a moment doubt the veracity of such a character ? — therefore 
different conjectures were made by different persons. Mr. Murdoch 
in particular gave a paper to the Royal Society in defence of Newton; 
but it was such as very little tended to clear up the matter. Philo- 
sophical Transactions^ vol: liii. p. 192. — Some have supposed that 
Newton made use of water strongly impregnated with Saccharum 
Saturni, because he mentions sometimes using such water, to increase 
the refraction, when he used water prisms instead of glass prisms. 
Newton s Optics, p. 62. — ^And others have supposed, that he tried the 
experiment with so strong a persuasion in his own mind, that the di- 
vergency of the colours was always in the same proportion to the mean 
refraction, in all sorts of refracting mediums, that he did not attend 
so much to that experiment as he ought to have done, or as he usually 
did. None of these suppositions having appeared at all satisfactory, I 
hav£ therefore endeavoured to find out the true cause of the difference, 

K 2 



76 Some Account of the Discovery made hy Mr. John Dollondy 

i , 

and thereby shew, how the experiment may be made to agree with 
Newton's description of it, and to get rid of those doubts, which 
have hitherto remained to be cleared up. 

It is well known, that in Newton's time the English were not the 
most famous for making optical instruments: — telescopes, opera-glasses, 
&c. were imported from Italy in great numbers, and particularly from 
Venice ; where was manufactured a kind of glass which was much more 
proper for optical purposes than any made in England at that time. The 
glass made at Venice was nearly of the same refractive quality as our 
crown glass, but of a much better colour, being sufficiently clear and 
transparent for the purpose of prisms. It is probable that Newton's 
prisms were made with this kind of glass ; and it appears to be the more 
so, because he mentions the specific gravity of common glass to be 
to water as 2.58 to 1. Newton s Opt. p. 247, which nearly answers 
to the specific gravity we find the Venetian glass generally to have. 
Having a very thick plate of this kind of glass, which was presented 
to me about twenty-five years ago by the late professor Allemand, of 
Leyden, and which he jthen informed me had been made many years, 
I cut a piece from this plate of glass to form a prism, which I conceived 
would be similar to those made use of by Newton himself. I 
have tried the Newtonian experiment with this prism, and find it 
answers so nearly to what Newton relates, that the difference which 
remains may very easily be supposed to arise from any little dif- 
ference, which may and does often happen in the same kind of glass 
made at the same place at different times. Now the glass prism 
made use of by Dollond to try the same experiment was made of 
English flint glass, the specific gravity of which I have never known 



relating to Refracting Telescopes. 77 

to be less than 3, 12. This difference in the densities of the prisms 
^ijsed by Newton and Dollond was sufficient to cause all the dif- 
fer^ice which appeared to the two experimenters in trying the same 
experiment. 

From this it appears, that Newton was accurate in this experiment 
as in all other?, and that his not having discovered that, \vhich was 
discovered by Dollond so many years afterwards, was owing intirely to 
accident; for if his prism had been made of glass of a greater or less 
density, he would certainly have then made the discovery, and refract- 
ing telescopes would not have remained so long in their original im- 
perfect state. 



78 



jin Attempt to explain a Difficultij in the Theory 
of' Vision, depending on the different Refrangi-^ 
hility of Light. By the Rev, Nevil Maskelyne^ 
D.D. F.R S. and Astronomer Royal. 



Read June 1 8, 1789. 

1 HE ideas of sight are so striking and beautiful, that we are apt to 
consider them as perfectly distinct. The celebrated Euler, taking this 
for granted, has supposed, in the Memoirs of the Royal Academy of 
Sciences at Berlin for 1747, that the several humours of the human 
eye were contrived in such a manner as to prevent the latitude of 
focus arising from the different refrangibility of light, and considers 
this as a new reason for admiring the structure of the «ye; for that 
a single transparent medium, of a proper figure, would have been 
sufficient to represent images of outward objects in an imperfect man- 
ner; but to make the organ of sight absolutely complete, it was 
necessary it should be composed of several transparent mediums. 



An Attempt to explain a Difficulty in the Theory of Vision ^ ^c. 79 

properly figured, and fitted together agreeable to the rules of the 
sublimest geometry, in order to obviate the effect of the different re- 
frangibility of light in disturbing the distinctness of the image ; and 
hence he concludes, that it is possible to dispose four refracting sur- 
faces, in such a manner as to bring all sorts of rays to one focus, at 
whatever distance the object be placed. He then assumes a certain 
hypothesis of refraction of the differently refrangible rays, and builds 
thereon an ingenious theory of an achromatic object-glass, composed 
of two meniscus glasses vi^ith v^^ater between them, with the help of an 
analytical calculation, simple and elegant, as his usually are. 

He has not, however, demonstrated the necessary existence of his 
hypothesis, his arguments for which are more metaphysical than 
geometrical ; and, as it was founded on no experiments, so those made 
since have shewn its fallacy, and that it does not obtain in nature. 
Moreover, which is rather extraordinary, it does not account, accord- 
ing to his own ideas, for the very phenomenon which first suggested • 
it to him, namely, the great distinctness of the human vision, as was 
observed to me, many years ago, by the late Mr. John Dollond, F.R.S. . 
to whom we are so much obliged for the invention of the achromatic 
telescope,'* for the refractions at the several humours of the eye. 



* As a misstatement of this fact has been made by both Paley and Priestley, we shall 
quote their own words for the satisfaction of the reader, — " At last it came into the 
mind of a sagacious optician, to inquire how this matter was managed in the eye; in 
which there was exactly the same difficulty to contend with, as in the telescope. His 
, observation taught him, that, in the eye, the evil was cured by combining together 
lenses composed of different substances, i. e. of substances which possessed different 



60 An Attempt to explain a Difficulty in the Theory of Vision^ 

being all made one way, the colours produced by the first refraction 
will be increased at the two subsequent ones instead of being corrected, 
whether we make use of Newton's or Euler's law of refraction of the 
differently refrangible rays. 

Thus Euler produced an hypothetical principle, neither fit for ren- 
dering a telescope achromatic, nor to account for the distinctness of 
the human vision; and the difficulty of reconciling that distinctness 
with the principle of the different refrangibility of light discovered by 
Sir Isaac Newton remains in full force. 

In order to go to the bottom of this difficulty, as the best probable 
means of obviating it, I have calculated the refractions of the mean, 
most, and least refrangible rays at the several humours of the eye, and 
thence inferred the diffusion of the rays, proceeding from a point in 
an object, at their falling upon the retina, and the external angle 
which such coloured image of a point upon the retina corresponds to. 



4 
refracting powers. Onr arHst borrowed from thence his hint ; and produced a correction 

of the defect, by imitating, in glasses made from different materials, the effects of the 

different humours through which the rays of light pass before they reach the bottom of 

the eye." — See Paley, p. 23. " M. Euler did not pretend to controvert the experiments 

of Newton ; but he said that they were not contrary to his hypothesis, but in so small a 

degree as might be neglected, and asserted that, if they were admitted in all their ' 

extent, it would be impossible to correct the difference of refrangibility occasioned by the 

transmission of the rays from one medium into another of different density ; a correction 

which, he thought,-was very possible, since he supposed it to be actually effected in the 

structure of the eye, which he thought was made to consist of different mediurqs for 

that very purpose. To this kind of reasoning Mr. DoUond made no reply ; but by 

appealing to the experiments of Newton, and the great circumspection with which it 

was known that he conducted all his inquiries." — See Priestley, p. 458. 



by the Rev. Dr. Maskelyne. 81 

I took the dimensions of the eye from M. Petit, as related by T)v. 
Jurin; and, the specific gravities of the aqueous and vitreous humours 
having been found tp'be nearly the same with that of water, and the 
refraction of the vitreous humour of an ox's eye having been found by 
Mr. Hawksbee to be the same as that of water, and the ratio of re- 
fraction out of air into the crystalline humour of an ox's eye having 
been found by the same accurate experimenter to be as 1 to ,68327, I 
took the refraction of the mean refrangible rays out of air into the 
aqueous or vitreous humour, the same as into water, as 1 to ,74853, 
or 1,33595 to i ; and out of air into the crystalline humour as 1 to 
,68327, or 1,46355 to 1. Hence I find, according to Sir Isaac New- 
ton's two theorems, related at Part II. of Book I. of Optics, p. 113^ 
that the ratio of refraction of the most, mean, and least refrangible 
rays at the cornea should be as 1 to ,74512, ,74853 and ,75197; at 
the fore-surface of the crystalline as 1 to ,91 173, ,91282, and ,91392; 
and at the hinder-surface of the crystalline as 1 to 1,09681, 1,09550, 
and 1,09420. 

Now, taking with Dr. Jurin 15 inches for the distance at which 
the generality of eyes in their mean state see with most distinctness, 
I find the rays from a point of an object so situate will be collected 
into three several foci, viz. the most, mean, and least refrangible 
rays at the respective distances behind the crystalline, ,5930, ,6034, 
and ,6141 of an inch, the focus of the most refrangible rays being 
,0211 inch short of the focus of the least refrangible ones. 

Moreover, assuming the diameter of the pencil of rays at the cor- 
nea, proceeding from the object at 15 inches distance, to be -i-th of 
an inch in a strong light, which is a large allowance for it, the semi- 



82 An Attempt to explain a Diffi,culty in the Theory oj Vision^ 

angle of the pencil of mean refrangible rays at their concourse upon 
the retina will be 7° 12-', whose tangent to the radius unity, or ,1264 
multiplied into ,0211 inch, the interval of the foci of the extreme re- 
frangible rays, gives ,002667 inch for the diffusion of the different 
coloured rays, or the diameter of the indistinct circle upon the retina. 
Now, I find, that the diameter of the image of an object upon the 
retina is to the object as ,6055 inch to the distance of the object from 
the centre of curvature of the cornea; or the size of the image is the 
same as would be formed by a very thin convex lens, whose focal dis- 
tance is, 6055 inch, and consequently a line in an object which subtends 
an angle of l' at the centre of the cornea will be represented on the 
retina by a line of -^gi^-^th inch. Hence the diameter of the indistinct 
circle on the retina before found, ,002667 will answer to an external 
angle of ,002667 X5 67 8'= 15' 8'', or every point in an object should 
appear to subtend an angle of about 15', on account of the different 
refrangibility of the rays of light. 

I shall now endeavour to shew that this angle of ocular aberration 
is compatible with the distinctness of our vision. This aberration is 
of the same kind as that which we experience in the common re- 
fracting telescope. Now, by computation from the tabular apertures 
and magnifying powers of such telescopes, it is certain that they admit 
of an angular indistinctness at the eye or no less than 57'; therefore 
the ocular aberration is near four times less than in a common refracting 
telescope, and consequently the real indistinctness, being as the square 
of the angular aberration, will be 14 or 15 times less in the eye than 
in a common refracting telescope, which may be easily allowed to be 
imperceptiWe. 



by the Rev. Dr, Maskelyne. 83 

Moreover, Sir Isaac Newton has observed, with respect to the 
like difficulty of accounting for the distinctness with which refracting 
telescopes represent objects, that the erring rays are not scattered 
uniformly over the circle of dissipation in the focus of the object- 
glass, but collected infinitely more densely in the centre than in any 
other part of the circle, and in the way from the centre to the cir- 
cumference grow continually rarer and rarer, so as at the circum- 
ference to become infinitely rare ; and by reason of their rarity are 
not strong enough to be visible, unless in the centre and very near it. 

He farther observes, that the most luminous of the prismatic 
colours are the yellow and orange, which ^ affect the sense more 
strongly than all the rest together; and next to these in strength are 
the red and green; and that the blue, indigo, and violet, compared 
with these, are much darker and fainter, and compared with 
the other stronger colours, little to be regarded; and that therefore 
the images of the objects are to be placed not in the focus of the 
mean refrangible rays, which are in the confine of green and blue, 
but in the middle of the orange and yellow, there where the colour is 
most luminous, that which is in the brightest yellow, that yellow which 
inclines more to orange than to green. 

From all these considerations, and by an elaborate calculation, he 
infers, that though the whole breadth of the image of a lucid point 
be -jiyth of the diameter of the aperture of the object-glass, yet the 
sensible image of the same is scarce broader than a circle whose dia- 
meter is -a-foth part of the diameter of the aperture of the object- 
glass of a good telescope; and hence he accounts for the apparent 
diameters of the fixed stars as observed with telescopes by astrono- 
mers, although in reality they are but points. 



84 An Attempt to explain a Difficulty in the Theory of Vision, 

The like reasoning is applicable to the circle of dissipation on the 
retina of the human eye; and therefore we may lessen the angular 
aberration, before computed at 15', in the ratio of 250 to 55, which 
will reduce it to 3' 18'". 

This reduced angle of aberration may perhaps be double the appa- 
rent diameter of the brightest fixed stars to an eye disposed for seeing 
most distinctly by parallel rays; or, if short-sighted, assisted by a pro- 
per concave lens; which may be thought a sufficient approximation in 
an explication grounded on a dissipation of rays, to which a precise 
limit cannot be assigned, on account of the continual increase of 
density from the circumference, to the centre. Certainly some such 
angle of aberration is necessary to account for the stars appearing 
under any sensible angle to such an eye; and if we were, without rea. 
son, to suppose the images on the retina to be perfect, we should be 
put to a much greater difficulty to account for the fixed stars appearing 
otherwise than as points, than we have now been to account for the 
actual distinctness of our sight. 

The less apparent diameter of the smaller fixed stars agrees also 
with this theory; for the less luminous the circle of dissipation is, the 
nearer we must look towards its centre to find rays sufficiently dense 
to move the sense. From Sir Isaac Newton's geometrical account of 
the relative density of the rays in the circle of dissipation, given in his 
system of the world, it may be inferred, that the apparent diameters 
of the fixed stars, as depending on this cause, are nearly as their 
whole quantity of light. 

In farther elucidation of this subject let me add my own experi- 
ment. When I look at the brighter fixed stars, at considerable 



by ike Rev. Dr, Maskelyne. * 85 

elevations, through a concave glass fitted, as I am short-sighted, to 
shew them with most distinctness, they appear to me without scintil- 
lation, and as a small round circle of fire of a sensible magnitude. If 
I look at them without the concave glass, or with one not suited to 
my eye, they appear to cast out rays of a determinate figure, not ex- 
actly the same in both eyes, somewhat like branches of trees (which 
doubtless arise from something in the construction of the eye) and to 
scintillate a little, if the air be not very clear. To see day objects 
with most distinctness, I require a less concave lens by one degree 
than for seeing the stars best by night, the cause of which seems to 
be, that the bottom of the eye being illuminated by the day objects, 
and thereby rendered a light ground, obscures the fainter colours blue 
indigo and violet in the circle of dissipation, and therefore the best 
image of the object will be found in the focus of the bright yellow 
rays, and not in that of the mean refrangible ones, or the dark green, 
agreeable to Newton's remark, and consequently nearer the retina of 
a short-sighted person ; but the parts of the retina surrounding the 
circle of dissipation of a star being in the dark, the fainter colours, 
blue, indigo, and violet, will have some share in forming the image, 
and consequently the focus will be shorter.- 

The apparent diameter of the stars here accounted for is different 
from that explained by Dr. Jurin, in his Essay on Distinct and In- 
distinct Vision, arising from the natural constitution of the generality 
of eyes to see objects most distinct at moderate distances, and few 
being capable of altering their conformation enough to see distant 
objects, and among them the celestial ones, with equal distinctness. 



60 An Att^pt to explain a Difficully in the Theory of Vision, 

But the cause of error, which I have pointed out, will affect all eye?, 
even those which are adapted to distant objects. 

If this attempt to shew the compatibility of the actual distinctness 
of our sight with the different rcfrangibility of light shall be admitted 
as just and convincing, we shall have fresh reason to admire the 
wisdom of the creator in so adapting the aperture of the pupil and the 
different rcfrangibility of light to each other, as to render the picture 
of objects upon the retina relatively, though not absolutely, perfect, 
and fitted for every useful purpose ; " where," to borrow the words of 
our religious and oratorical philosopher Derham, " all the glories of 
the heavens and earth are brought and exquisitely pictured." 

Nor does it appear, that any material advantage would have been 
obtained, if the image of objects on the retina had been made ab- 
solutely perfect, unless the acuteness of the optic nerve should have 
been increased at the same time; as the minimum visihile depends no 
less on that circumstance than the other. But that the sensibility of 
the optic nerve could not have been much increased beyond what it is, 
without great inconvenience to us, may be easily conceived, if we only 
consider the forcible impression made on our eye by a bright sky, or 
even the day objects illuminated by a strong sun. Hence we may 
conclude, that such an alteration would have rendered our sight pain- 
ful instead of pleasant, and noxious instead of useful. We might 
indeed have been enabled to see more in the starry heavens with the 
naked eye, but it must have been at the expence of our daily labours 
and occupations, the immediate and necessary employment of man. 
I shall only mention farther, and obviate an objection to the dif- 



hy the Rev. Dr, Maskelyne, BT 

fusion of the rays upon the retina by the different refrangibility of 
light. It may be said, that the ocular aberration, being a separate 
cause from any effect of the telescope, should subsist equally when we 
observe a star through a telescope as wheh we look at it with the 
naked eye; and that therefore the fixed stars could not appear so 
small as they have been found to do through the best telescopes, and 
particularly by Dr. Herschel with his excellent ones. To this I answer, 
that the ocular aberration, which is proportional to the diameter of 
the pupil when we use the naked eye, is proportional to the diameter 
of the pencil of rays at the eye when we look through a telescope, 
which being many times less than that of the pupil itself, the ocular 
aberration will be diminished in proportion, and become insensible. 



86 



jiii Account of an Improvement made by Mr. Peter 
DoUond in his New Telescopes. In a Letter 
^o James Short, M.A. F.R. S. with a Letter of 
Mr. Short's to the Rev. Thomas Birch, D.D. 
S^ecref. R. S. ' 

DEAR SIR, 

1 HAVE sent you inclosed, a letter which I received 
this morning from Mr. Dollond, concerning an improvement which 
he has made in his new telescopes. He, some months ago, sent me 
a telescope, in this new way, of 3 J feet focal length, with an aperture 
of 3f Inches; I examined it, and I approved of it; I have tried it 
with a magnifying power of 150 times, and I found the image distinct, 
bright, and free from colours. 

You may, if you please, lay Mr. Dollond's letter before the Royal 
Society. 

I am, DEAR SIR, 

Your most obedient and humble servant, 

James Short. 

Surrey Street, 
February 7, 1765. - 



89 



Mr. DolloncTs Letter to Mr. Short. 



Read February 7, 1765. 

SIR, ,, 

1 TAKE the liberty of sending you the following 
short account of an improvement I have lately made in the compound 
object glasses of refracting telescopes. 

The dissipation of the rays of light may be perfectly corrected in 
object glasses, by combining mediums of different refractive qualities; 
and the errors or aberrations of the spherical surfaces may be corrected 
by the contrary refractions of two lenses, made of the different me- 
diums; yet as the excess of refraction is in the convex len&, and 
though the surfaces of the concave lens may be so proportioned as to 
aberrate exactly equal to the convex lens, near the axis; yet as the 
refractions of the two lenses are not equal, the equality of the aber- 
rations cannot be continued to any great distance from the axis. 

In the year 1758, when my father had constructed some object 
glasses for telescopes in this manner, viz. with one convex lens of 
crown glass, and one concave lens of white flint glass; he attempted 

M 



£0 An Accounl of an Improvement made by Mr. Peter Dollond, 

to make short object glasses to be used with concave eye glasses, in 
the same manner; but as the field of view, in using a concave eye 
glass depends on the aperture of the object glass, the limits of the 
aperture were found to be too small: this led my father to consider 
that if the refraction of the crown glass (in which the excess was) 
should be divided by means of having two lenses made of crown 
glass instead of one, the aberration would thereby be decreased, and 
the apertures might then be larger : this was tried with success in 
those object glasses, when concave eye glasses were used, and these 
have been ever since made in this manner : some trials were likewise 
made, at the same time, to enlarge the apertures of longer object 
glasses, where convex eye glasses were used, by the same method ; 
but these not succeeding, in the same manner, the method of making 
them with one lens of crown glass, and one of white flint glass, was 
continued. 

As I could not see any good reason why the method, which was 
practised with so much success, when concave eye glasses were used, 
should not do with convex ones ; I determined to try some further 
experiments in that way. After a few trials, I found it might be 
done; and in a short time I finished an object glass of 5 feet focal 
length, with an aperture of 3:| inches, composed of two convex lenses 
of crown glass, and one concave of white flint glass. 

Thinking that the apertures might be yet admitted larger; I at- 
tempted to make one of 3 J feet focal length, with the same aperture 
of 3f inches, which I have now completed, and am ready to show 
the same to the Royal Society, if desired. 

The difliculty of procuring good glass of so large a diameter, and 



in his New Telescopes. gi 

of the thickness required, added to the great exactness of the sur- 
faces, in order to correct the aberration in such large apertures, has 
prevented me from attempting to extend them any farther in that 
lerigth. 

I am, SIR, 

Your most obedient, 

and most humble servant, 

Peter DoUond. 



M 2 



m 



A Letter J^rom Mr. Peter DoUond, to Nevil Mas- 
kelyne, F.R.S. &^ Astronomer Royal; describing 
some Additions cmd Alterations made to Hadley's 
Quadrant, to render it more serviceable at Sea. 



Read March 29, 1772. 



REVEREND SIR, 

■\ 

xHE particular attention which you have always 

shown to any improvement tending to the advantage of astronomy 

or navigation, makes me take the liberty to trouble you with an ac- 

* count of some additions and alterations which I have lately made 

to the Hadley's quadrant. 

The general use of this instrument at sea is so well known, that no 
mention need be made of the importance of any improvements in 
the construction, that may render the observations more exact, and 
occasion more frequent opportunities of making them. 



Description of some j^dditionSj §c. to Hadley's Quadrant. 93 

The glasses of the Hadley's quadrant should have their two surfaces 
perfect planes, and perfectly parallel to each other. From several 
years practice in grinding these glasses, I have found out methods of 
making them to great exactness; but the advantage, that should arise 
from the goodness of the glasses, has often times been defeated by 
the index glass being bent by the brass frame that contains it: to 
prevent this, I have contrived the frame, so that the glass lies on 
three points, and the part that presses against the front of the glass 
has also three points exactly opposite to the former. These points 
are made to confine the glass by three screws at the back, that act 
exactly opposite to the points between which the glass is placed* 
This little contrivance may be of some use; but the principal im- 
provements are in the methods of adjusting the glasses, particularly 
for the back observation. 

The method hitherto practised for adjusting that part of the instru- 
ment, by means of the opposite horizons at sea, has been attended 
with so many difficulties that it has scarcely ever been used ; for so lit- 
tle dependance could be placed on the observations taken this way, 
that the best Hadley's sextants made for the purposes of observing 
the distances of the moon from the sun or fixed stars, have been 
always made without the horizon glass for the back observation ; for 
want of which, many valuable observations of the sun and moon have 
been lost, when their distance has exceeded 120 degrees. 

To make the adjustment of the back observation easy and exact, I 
have applied an index to the back horizon glass, by which it may be 
moved into a parallel position to the index glass, in order to give it 
the two adjustments, in the same manner as the fore horizon glass is 



94 Description of &ome Additions f ^c. (o Hadley's Quadrant, 

adjusted. Then, by moving the index to which the back horizon 
glass is fixed, exactly 90 degrees (which is known by the divisions 
made for that purpose) the glass will be thereby set at right angles 
to the index glass, and consequently will be properly adjusted for use, 
and the observations may be made with the same accuracy by this, 
as by the fore observation. 

To adjust the horizon glasses in the perpendicular position to the 
plane of the instrument, I have contrived to move each of them by 
a single screw, that goes through the frame of the quadrant, and is 
turned by means of a milled head at the back, which may be done 
by the observer while he is looking at the object. 

To these improvements. Sir, I have added your method of placing 
darkening glasses behind the horizon glasses, which you have been 
«o ki^d as to give me liberty to apply to my instruments. These 
glasses, which serve for darkening the object seen by direct vision, 
in adjusting the instrument by the sun or moon, I have placed in 
such a manner as to be turned behind the fore horizon glass, or be- 
hind the back horizon glass, that they may be used with either; there 
are three of these glasses of different degrees of darkness; the 
lightest or palest I do imagine will be of use in taking the sun's alti- 
tude when ihe horizon appears glaring, which I believe often happens 
by the reflection of the sea. 

If these additions and alterations should be thought to be real im- 
provements, which I cannot doubt. Sir, if they are honoured with 
your approbation, I hope they may serve in conjunction with those 
improvements you have made yourself in respect to the obviating any 
possible errors in the parallelism of the planes of the index glass, and 



to render it more serviceable at Sea. 95 

in regard to the adjustment of the telescope parallel to the plane of 
the quadrant, to extend the use of this most valuable nautical instru- 
ment, and to add to the exactness of the celestial observations taken 
with it to determine the longitude at sea. But of these particulars I 
need say no more, since you are, v^^ithout doubt, in every respect, 
the properest person to give an account of them. 

. I am, SIR, 

Your most obedient, 

humble servant, 

Peter DoUond. 

London, 
Februaiy 25, 1772. 



96 



RemarJcs on the Hadley's Quadrant, tending prin- 
dpally to remove the Difficulties which have 
hitherto attended the Use of the Back-observation, 
and to obviate the Errors that might arise J^rom 
a Want of Parallelism in the two Surfaces of 
the Index-Glass. By Nevil Maskelyne, F.R.S. 
Astronomer Royal. 



Read May 28, 1772. 

X H£ back-observation with Hadley's quadrant being founded on the 
same principles, and in theory, equally perfect with the fore observa- 
tion, and being at the same time necessary to extend the use of the 
instrument up to 180 degrees (it being impracticable to measure 
angles with any convenience beyond 120 degrees with the fore- 
observation) it may seem surprizing that it hath not been brought 
equally into general use, more especially since the method of finding 
the longitude by observations of the moon, has been practised at sea 
for some years past; since this method v^^ould receive considerable 



Remarks on the Hadleys Quadrant^ 8^e. 97 

advantage from the use- of the back-observation in taking distances 
of the sun and. nnoon between the first and last quarter, could such 
observations be as much depended upon as the fore-observation. The 
causes of this seem to have been principally these two, the difficulty 
of adjusting the back-horizon-glass, and the want of a method of 
directing, the sight parallel to the plane of the quadrant. The back- 
horizon-glass, like the fore-one, requires two adjustments : — the first, 
or common one, disposes it at right angles to the index glass, when 
the index stands at (O) upon the arch; which is usually performed by 
setting (0) of the index of the arch of the quadrant by double the 
dip of the horizon of the sea, and then holding the quadrant vertical 
with the arch downwards, and turning the back-horizon-glass about, 
by means of its lever or perpetual screw, till the reflected back-horizon 
appears to coincide with the fore-horizon seen directly. But this 
operation is so difficult in practice with the back -horizon-glass wholly 
silvered, except a small transparent slit in the middle, as it has been 
usually made, that few (if any) persons have ever received proper sa- 
tisfaction from it. If the back-horizon-glass was silvered in every 
respect like the fore-horizon-glass (which it ought to be) the upper 
part being left unsilvered, and a telescope was applied to it, perhaps 
this adjustment might be rendered somewhat easier and more exact; 
but it could not even thus be made so exact as the adjustment of the 
fore-horizon-glass may, by making use of the sun's limbs. 

The second adjustment of the back-horizon-glass, in the common 
construction of the quadrant, is still more troublesome, since it cannot 
be executed without setting the index 90 degrees off the arch, in or- 
der to place the index-glass parallel to the back-horizoR-gla33 ; when 

N 



98 Remarks on the Hadlefifs QuadrOntf 

this adjustment may be performed in the same manner as the corres- 
ponding adjustment of the fore-horizon-glass. But the bending of 
the index, that follows the setting it oiF the arch, is a very disagree- 
able circumstance, having a tendency, especially on board of ship, to 
expose both the index and centre work to damage ; and may even, 
without extraordinary precautions taken by the instrument maker in 
placing the plane of the index-glass exactly according to the length 
of the index, disturb its perpendicularity to the plane of the quadrant : 
on these accounts it would be much better if this adjustment of the 
back-horizon-glass could be performed, like those of the fore-horizon- 
glass, with the index remaining upon the arch of the quadrant. 
Fortunately, this desideratum has been lately effected by an ingenious 
contrivance invented by Mr. Dollond, which he has given an account 
of in a letter addressed to me*, which I have presented to this So- 
ciety, by means of an additional index applied to the back- 
horizon-glass; whereby both the adjustments may be made by the 
same observations and with nearly the same exactness as those of the 
fore- horizon-glass: — for a further knowledge of which see the account 
itself. , ^ 

Besides the difficulty of adjusting the back-horizon -glass, the 
want of a method of directing the line of sight parallel to the plane 
of the quadrant has proved also a considerable obstacle to the use of 
the back-observation : this will easily appear from the following pro- 
position, that the error of the angle measured arising from any small 
deviation of the visual ray from a parallelism to the plane of the quad- 

* See page 92 for the Letter alluded to. 



by the Rev. Dr. Maskelyne. 99 

rant, is to twice an arch equal to the verse-sine of the deviation, as 
the tangent of half the angle measured by the quadrant is to radius, 
very nearly. Thus a deviation of 1° in the line of sight, will pro- 
duce an error of about l' in measuring an angle of 90°, whether by 
the fore or back-observation ; but the same deviation will produce an 
error of 4' in measuring an angle of 150°, of & in taking an angle 
of 160°, and 12' in taking an angle of 170°. Hence a pretty 
exact adjustment of the line of sight, or axis of the telescope, 
is requisite in measuring large angles, such as those are taken by the 
back-observation : and therefore a director of the sight ought by no 
means to be omitted in the construction of the instrument (as it 
commonly has been since Mr. Hadley's time, though recommended 
by him), except a telescope be made use of, which, if rightly placed, 
answers the same purpose better, especially in observing the distance 
of the moon from the sun between the first and last quarter. The 
director of the sight may be placed exact enough by construction ; 
but the telescope cannot, and Mr. Hadley, not having been aware 
ef the importance of an exact position of it, has accordingly given 
no directions for the placing of it. I shall therefore endeavour to 
supply this defect in the following remarks. 

In the first place, I would by all means recommend an adjusting 
piece to be applied to the telescope, whereby its axis may be brought 
parallel to the plane of the quadrant: in the next place, the back- 
horizon-glass ought to be silvered in the same manner as the fore- 
horizon-glass : and thirdly, two thick silver wires should be placed 
within the eye-tube in the focus of the eye-glass parallel to one 
another, and to the plane of the quadrant. If tHey were put at such 

N 2 



100 Remarks on the Hadleifs Quadrant y 

a distance as to divide the diameter of the field of view into three 
equal parts, it might be as convenient as any other interval. In this 
manner wires were placed in the telescope by Mr. Hadley, as appears 
by his accountof the instrument in Philosophical Transactions, No. 420. 
These wires are to be adjusted parallel to the plane of the quadrant, by 
turning the eye-tube round about which contains the wires, till they 
appear parallel to the plane of the quadrant. The axis of the teles- 
cope, by which is meant the line joining the centre of the object-glass 
and the middle point between the two wires, is to be adjusted parallel 
to the plane of the quadrant by either of the two following methods. 

Method I. — When the distance of the moon from the sun is 
greater than QO degrees, by giving a sweep with the quadrant and 
moving the index, bring the nearest limbs to touch one another at 
the wire nearest the plane of the quadrant. Then, the index re- 
maining unmoved, make the like observation at the wire farthest from 
the plane of the quadrant; and note whether the nearest limbs are in 
contact as they were at the other wire: if they are, the axis of the 
telescope is parallel to the plane of the quadrant: but if they are not, 
it is inclined to the same, and must be corrected as follows. If the 
nearest limbs of the sun and moon seem to lap over one another at 
the wire farthest from the plane of the quadrant, the object end of 
the telescope is inclined from the plane of the quadrant, and must be 
altered by the adjustment made for that purpose : but, if the nearest 
limbs of the sun and moon do not come to touch one another at the 
wire farthest from the plane of the quadrant, the object end of the 
telescope is inclined towards the plane of the quadrant, and must be 
altered by the adjustment accordingly. Let these operations be re- 



by the Rev. Dr. Maskelyne. 101 

peated until the observation is the same at both the parallel wires, 
and the axis of the telescope will be adjusted parallel to the plane 
of the quadrant. In like manner, the axis of the telescope may be 
also adjusted parallel to the plane of the quadrant for the fore-observa- 
tion. 

Method II. — Set the index to (o) and hold the plane of the quadrant 
parallel to the horizon of the sea, with the divided arch upwards, the 
two wires being parallel to, and including both the direct fore-horizon, 
and the reflected back-horizon, between them. Raise or lower the 
plane of the quadrant until the direct and reflected horizons coincide 
together: if the coincidence happens in the middle between the two 
wires, or rather, to be more exact, above the middle by such a part of 
the field of view as answers to the number of minutes in the de- 
pression of the horizon .(which may be easily estimated if the angular 
interval of the wires be first found by experiment, in manner here- 
after mentioned) the axis of the telescope is parallel to the plane of 
the quadrant ; but if it does not, the line of sight is inclined to the 
plane of the quadrant, and must be corrected as follows. If the direct 
and reflected horizons, when they coincide, appear higher above the 
middle between the wires, than what the quantity of the depression 
of the horizon amounts to, the object end of the telescope is inclined 
from the plane of the quadrant, and must be altered by the adjust- 
ment made for that purpose; but if the two horizqns appear to 
coincide in a lower part of the field of the telescope, the object end 
of the telescope is inclined towards the plane of the quadrant, and 
must be altered by the adjustment accordingly. Repeat these ope- 
rations till the two horizons appear to coincide above the middle between 



102 Remarks on the Hadleys Quadrant, 

the two wires, by the quantity of the depression of the horizon, and 
the axis of the telescope will be adjusted parallel to the plane of the quad- 
rant. In order to find the angular interval between the wires, hold the 
quadrant perpendicular to the horizon, as in observing altitudes ; and 
turn about the eye-tube with the wires until they are parallel to, and in- 
clude the direct fore-horizon and reflected back-horizon between them. 
Move the index from (o) along the divided arch, at the same time 
taising or lowering the telescope by the motion of the quadrant until 
the direct horizon appears to coincide with the upper wire, and the 
reflected back-horizon with the lower wire ; the number of degrees 
and minutes shown upon the arch, increased by double the depression 
of the horizon, will be the angular interval of the wires ; its propor- 
tion to the depression of the horizon will be therefore known ; and 
hence the space in the field of the telescope answering to the depres- 
sion of the horizon, may be easily estimated near enough for 
adjusting the axis of the telescope in the manner before mentioned. 
The first of the two methods here given for adjusting the position of 
the telescope will probably be found most convenient ; and the greater 
Xhe distance of the sun and moon is, the more nearly may the adjust- 
ment be made, because the same deviation of the axis of the 
telescope will cause a greater error. 

The telescope should be fixed by the instrument-maker so as to 
command a full field of view when the instrument is placed at 90® 
if the instrument be an octant, or 120° if it be a sextant ; because 
the index-glass then stands more oblique with respect to the incident 
and reflected rays, and consequently the field of view of the telescope, 
as far as it depends upon the index-glass, will be more contracted 



by the Rev. Dr. Maskelyne, 103 

tlian in any other position of the index: but if there is a fait field of 
•view in this case, there necessarily must be so in every other position 
of the index. 

The two parallel wires will be very useful on many occasions, as 
well in the fore as the back-observation. In taking the altitude of 
the sun, moon, or star, direct the sight towards the part of the 
horizon underneath, or opposite to the object, according as you 
intend to observe by the fore or back- observation, a^nd hold the 
quadrant that the wires may constantly appear perpendicular to the 
horizon, and move the index till you see the object come down 
towards tlie horizon in the fore-observation, or up to it in the 
back-observation,, and turn the instrument in order to bring the 
object between the wires ; then move the index till the sun 
or moon's limb, or the star touch the horizon. The nearer 
the object is brought to an imaginary line in the middle between 
the wires (it is indifferent what part of the line it is brought 
to) and the truer the wires are kept perpendicular to the horizon, 
the more exact will the observation be. In the fore-observation, the 
object appears in its real position ; but in the back-observation, the 
object being brought through the zenith to the horizon, the real 
upper-limb will appear the lowest ; and the contrary. Either limb 
of the sun may be used in either observation ; but it will be most 
convenient in general to make the sun appear against the sky, and not 
against the sea ; and then the objects appearing inverted through the 
telescope, the sun will appear lowest, and the horizon highest. The 
observed altitude is to be corrected for dip, refraction, and sun's 
semi -diameter, as usual. 



104 Remarks on the Hadleys Quadrant^ 

In taking the distance of the nearest limbs of the sun and moon, 
whether by the fore or back-observation, having 'first set the index 
to the distance nearly, by the help of the Nautical Almanac, and 
brought the moon to appear anywhere on or near the diameter of the 
field of view of the telescope, which bisects the interval between the 
wi^es, give a sweep to the quadrant, and the sun and moon will pass 
by one another ; if in this motion the nearest limbs, at their nearest 
approach, just come to touch one another, without lapping over, on 
or near any part of the diameter of the field of the. telescope which 
bisects the interval between the wires, the index is rightly set ; but if 
the nearest limbs either do not come to meet, or lap over one another, 
alter the index, and repeat the observation till the nearest limbs come 
to touch one another properly. This method of observing will be 
found much more easy and expeditious than without the wires, since 
in that case it would be necessary to make the limbs touch very near 
the centre of the telescope, but here it is only necessary to make 
them do so anywhere on or near the diameter of the field of the 
telescope which bisects the interval between the two wires. 

The same method may be used in taking the moon's distance from 
a fixed star. 

It may not be amiss here to make some remarks on the rules that 
have been usually given for observing the sun's altitude, both with the 
fore and back-observation, which have all been defective, and to point 
out the proper directions to be followed, when a telescope is not used 
w'ith two parallel wires to direct the quadrant perpendicular to the 
horizon, and to shew the principles on which these directions are 
founded. 



hy the Rev. Dr. Maskelyne, 105 

Observers are commonly told, that in making the fore-observation 
they should move the index to bring the sun down to the part of the 
horizon directly beneath them, and turn the quadrant about upon the 
axis of vision ; and when the sun touches the horizon at the lowest 
part of the arch described by them, the quadrant will shew the 
altitude above the visible horizon. I allow that this rule would be 
true, if a person could by sight certainly know the part of the hori- 
zon exactly beneath the sun ; but, as this is impossible, the precept 
is incomplete. Moreover, in taking the sun's altitude in or near the 
zenith, this rule intirely fails, and the best observers advise to hold 
the quadrant vertical, and turn one's self about upon the heel, stop- 
ping when the sun glides along the horizon without cutting it : and it 
is certain that this is a good rule in this case, and capable with care of 
answering the intended purpose. We have thus t^yo rules for the 
same thing, which is a proof that neither of them is an universal one, 
or sufficient in all cases alone. 

In taking the back-observation, observers have been advised either 
to turn the quadrant about upon the axis of vision, or, holding the 
quadrant upright, to turn themselves about upon the heel, indifferently. 
The true state of the case is this; that, in taking the sun's altitude, 
whether by the fore or back-observation, these two methods must be 
combined together; that is to say, the observer must turn the quad- 
rant about upon the axis of vision, and at the same time turn himself 
about upon his heel, so as to keep the sun always in that part of the 
horizon-glass which is at the same distance as the eye from the plane 
of the quadrant: for, unless the caution of observing the objects in 
the proper part of the horizon-glass be attended to, it is evident the 



106 Remarks on the Hadley's Quadrant, 

angles measured cannot be true ones. In this way the reflected sun^ill 
describe an arch of a parallel circle round the true sun, whose convex 
side will be downwards in the fore-observation, and upwards in the 
back-observation, and consequently, when, by moving the index, the 
lowest point of th6 arch in the fore-observation, or the uppermost 
point of the arch in the back-observation, is made to touch the hori- 
zon, the quadrant will stand in a vertical plane, and the altitude above 
the visible horizon will be properly observed. 

The reason of these operations may be thus explained: — the image 
of the sun being always kept in the axis of vision, the index will al- 
ways show on the quadrant the distance between the sun and any 
object seen directly which its image appears to touch; therefore, as 
long as the index remains unmoved, the image of the sun will de- 
scribe an arch everywhere equidistant from the sun in the heavens, 
and consequently a parallel circle about the sun, as a pole ; such a 
translation of the sun's image can only be produced by the quadrant 
being turned about upon a line drawn from the eye to the sun, as an 
axis ; a motion of rotation upon this line may be resolved into two, 
one upon the axis of vision, and the other upon a line on the qua- 
drant perpendicular to the axis of vision ; and consequently a proper 
combination of these two motions will keep the image of the sun 
constantly in the axis of vision, and cause both jointly to run over a 
parallel circle about the sun in the heavens ; but when the quadrant is 
vertical, a line thereon perpendicular to the axis of vision becomes a 
vertical axis ; and, as a small motion of the quadrant is all that is 
wanted, it will never differ much in practice from a vertical axis; 
therefore the observer, by properly combining and proportioning two 



by the Rev. Dr. Maskeli/ne. 107 

motions, one of the quadrant upon the axis of vision, and the other 
of himself upon his heel, keeping himself upright (which gives the 
quadrant a motion upon a vertical axis) will cause the image of the 
sun to describe a small arch of a parallel circle about the sun in the 
heavens, without departing considerably from the axis of vision. 

If it should be asked, why the observer should be directed to perform 
two motions rather than the single one equivalent to them on a line 
drawn from the eye to the sun as an axis, I answer, that we are not capa- 
ble, while Iboking^ towards the horizon, of judging how to turn the 
quadrant about upon the elevated line going to the sun as an axis, by 
any other means than by combining the two motions above-mentioned, 
SK> as to keep the sun's image always in the proper part of the horizon- 
glass. When the sun is near the horizon, the line going from the 
eye to the sun will not be far removed fromt the axis of vision; and 
consequently the principal motion of the quadrant will he performed 
on the axis of vision, and the part of the motion made on the vertical 
ams will be but small. On the contrary, when the s^in. is near the 
zenith, the line going to the; sun is not far. removed from a vertical 
line, and consequently the principal motion oi the quadrant will be 
performed on. a.vertipal axis, by the observer's turning himself about, 
and the part of the motion made on the axis of vision will be but 
Sflfiall. In intermediate altitudes of the sun, the motions of the qua- 
drant QU: the. ax,is of vision and on a vertical axis will be qiore ^ually 
4ivided. Hence appears the reason of the method used by the best 
observers in taking the sun's altitude when, near the zenith by hold- 
ing the quadrant vertical and turning about upon the heel, and the 

q % 



108 Remarks on the Hadleifs Quadrant, 

defects of the rules that have been commonly given for observing 
altitudes in other cases. 

As it may conduce to the setting this matter in a still clearer light, 
I shall here describe in order the several motions that will be given to 
the reflected image, by turning the quadrant about upon the axis of 
vision, a vertical axis, or the line drawn from the eye to the sun, 
successively. 

I. If the quadrant is turned about upon the axis of vision, the 
same being directed to the point of the horizon exactly beneath 
or opposite the sun, the image of the sun will move from right 
to left, or from left to right, across the horizon-glass, the same 
way as the arch of the quadrant is carried, both in the fore and 
back-observations, with a velocity which is to the angular velocity 
of the quadrant as the sine of the sun's altitude to the radius, 
describing an arch convex downwards in both cases; and when 
the motion of the sun in this arch is parallel to the horizon, the 
quadrant is held truly perpendicular to the horizon, and conse- 
quently in a proper position for taking the sun's altitude. But, 
if the axis of vision be directed to, and turned round a point in 
the horizon beside the vertical circle passing through the sun, the 
sun*s image, when its motion is parallel to the horizon, will be 
neither in the axis of vision nor the sun's vertical, but between 
both; at the same time, the plane of the quadrant will not be 
vertical, and [^the altitude found by bringing the sun's image to 
touch the horizon will not be the true altitude. 
II. If the quadrant be held perpendicular to the horizon, and turned 



by the Rev. Dr. Maskelyne. lo^ 

about upon a vertical axis, or one nearly so, the sun will describe 
an arch convex downwards in the fore-observation, and upwards 
in the back-observation, the motion of the sun being the same 
way as the axis of vision is carried in both cases, and being to 
the angular motion of the quadrant, as the verse-sine of the sun s 
altitude to the radius in the fore-observation, but as the verse- 
sine of the supplement of the sun's altitude to 180° to the radius 
in the back-observation. The sun therefore will move slower 
than the axis of vision in the fore-observation, and consequently 
will be left behind, with respect to the axis of vision, or seem to 
move backwards; and the sun will move quicker than the axis of 
vision in the back-observation, or will seem to get before it. 
When the motion of the sun in this arch is parallel to the horizon, 
the plane of the quadrant coincides with the vertical circle passing 
through the sun, and consequently the quadrant is in a proper 

• position for taking the sun's altitude. But if the quadrant be 
held a little deviating from the perpendicular position to the hori- 
zon, and turned about upon an axis, either vertical or only 
nearly so, the arch described by the sun apparently will cut the 
horizon, but will never move parallel to it, and consequently the 
quadrant will not be brought into a proper position for observing 
the sun's altitude. 

III. If the quadrant be turned on the line going to the sun as an 
axis, the reflected sun will be kept constantly in the axis of vision, 
and will describe an arch of a parallel circle about the real sun, 
with a velocity which is to the angular motion of the quadrant, 
as the sine of the suji's altitude is to the radius; and when the 



1 10 Remarks on the Hadleijs Quadrant , 

motion of the reflected sun is parallel to the horizon, the quad- 
rant is vertical. 

Hence naturally arise the three methods of taking an altitude, 
which have been mentioned before. In the first, the axis of vision is 
supposed; always directed to one and the same part of the horizon, 
aamely, that which is in the sun's vertical. In the second, the ob- 
Sjerver is required to hold the quadrant truly vertical, and to turn 
himself upon a vertical axis ; but it is evident neither of these motions 
can be accurately performed. In the third method, the observer is 
only required to move both himself and the quadrant, so as to keep 
the sun always in or near the axis of vision, which may be performed 
very well, because the axis of vision is a visible and certain direction 
for it. One exception, however, should be made tO; this general rule, 
namely, in taking the sun*s altitude when very lowj by the back- 
observation: in which case ijt will be best to use the second method, 
OX, else, to hold the quadrant, perpendicular by judgment; which will 
l)e:much facilitated by using a telescope containing wires; in ijts focus 
parallel to the plane: of; the quadrant, as described in p. 103 of this 
^ppmdisQ.:. for, in this- case,^ thq perpendicular position, of the qua- 
4rant cannot be; attained 5q near by thq method of; turning the 
quadrant on a line going to the sun as an axis,, as it can by any other 

^aethod^ 

Xt remains tptfTeatof the; errors which may arise from a defect of 
parallelism in thor two sarfaces; of the indexrglags, and to: pqintiQiit the 
means of obviating themi in the; celestial; observations. It? ig well 
k«o>vj?i. that, if 3j pe»pilt oC parallel ^a^s^ fells upoi^i, a^ glass wtoe two 



% the iRev, Dr. Maskelyne. 1 1 1 

surfaces are inclined to one another, and some of the rays are reflected 
at the fore-surface, and others passing into the glass and suffering a 
reflection at the back-surface and two refractions at the fore-surfac6 
emerge again from the glass, these latter rays will not be parallel t6 
those reflected at the fore-surface, as they would have been if the 
surfaces of the glass had been parallel, but will be inclined to the 
same. I find that the angle of their mutual inclination, which may 
be called the deviation of the rays reflected from the back-surface, 
will be to double the inclination of the surfaces of the glass (which is 
here supposed to be but small), as the tangent of the angle of inci- 
dence Out of air into glass, is to the tangent of the angle of refraction. 
Hence, in rays falling near the perpendicular, the deviation will be 
about three times the inclination of the surfaces ; and if the angles 
of incidence be 50°, 6o°, 70°, 80° or 85°, the deviations of the re- 
flected rays will be about 4, 5, 7, 13, or 26 times the inclination of 
the surfaces, respectively. Had the deviation been the same at all 
incidences of the rays on the index-glass, no error would have been 
produced in the observation ; because the course of the ray would 
have been equally affected in the adjustment of the instrument, as in 
the observation. But, from what has been just laid down, this is far 
from being the case, the deviation increasing according to the obli- 
quity with which the rays fall upon the index-glass ; so that in very 
oblique incidences of the rays, such as happen in measuring a large 
angle by the fore-observation or a small angle by the back-observation, 
the least defect in the parallelism of the planes of the two surfaces oi 
the index glass may produce a sensible error in the observation. 
What is here said only takes place in the fullest extent, if the 



112 ■" Remarks on the Hadler/s Quadrant, 

thickest or thinnest edge of the index -glass, or, to express the same 
thing in other words, the common section of the planes of the 
surfaces of the index-glass stands perpendicular to the plane of the 
quadrant; but, if the common section of the planes is inclined to 
the plane of the quadrant, the error arising from the defect of the 
parallelism of the surfaces will be lessened in the proportion of the 
sine of the inclination to the radius ; so that at last, when the 
common section becomes parallel to the plane of the quadrant, the 
error .entirely vanishes. For this reason : Mr. Hadley very properly 
directed the thickest and thinnest edges of the index-glass to be placed 
parallel to the plane of the quadrant. But as it may well be ques- 
tioned whether this care is always taken by the instrument-maker, and 
it cannot be supposed that the glasses can be ground perfect parallel 
planes, it would certainly be an advantage acquired to the instrument, 
could the error arising from a want of parallelism of the planes be 
removed in whatever position the common section of the planes 
should be placed with respect to the plane of the quadrant. This will 
be effected for celestial observations, if the upper part of the index- 
glass be left unsilvered on the back, and made rough and blacked, the 
lower part of the glass being silvered as usual, which must be covered 
whenever any celestial observations ar© made. Then, if the teles- 
cope be sufficiently raised above the plane of the quadrant, it is 
evident that the observations will be made by the rays reflected from 
the fore-surface of the upper part of the index-glass, and consequently, 
if the quadrant be adjusted by making use of the same part of the 
index-glass, the observations will be true, whether the two surfaces of 
the index-glass be parallel planes or not. The sun or moon may 



hy the Rev, Dr. Mashelyne, ,113 

be thus observed by reflection from the unsilvered parts of the index- 
glass and horizon -glass, so that a paler darkening glass will suffice, 
and they will appear much distincter than from an index-glass wholly 
silvered with a deep darkening glass ; for although the surfaces of a 
glass may be parallel, yet there always arises some little confusion from 
the double reflection. Neither will the moon appear too weak by two 
unsilvered reflections, even when her crescent is very small,- except 
she should be hazy or clouded; and then the light may be increased 
by lowering the telescope so as to take in part of the silvered reflection ^ 
of the index-glass, which in this case must be uncovered: the same is 
also to be understood with respect to the sun, should his light be too 
much weakened by haziness or thin clouds. The horizon-glasses 
should be adjusted, or the error of adjustment found by the sun or 
moon; the first will be in general the best object for the purpose; 
and, as the sun or moon seen directly through the unsilvered part of 
the horizon-glass will be much brighter than the image of the same 
seen by two unsilvered reflections, it must be weakened by a darken- 
ing glass placed beyond the horizon-glass, the reflected image being 
farther weakened, if necessary, by a paler darkening glass placed in 
the usual manner between the index-glass and the horizon-glass. 

If a quadrant was designed principally for taking the distance of 
the moon from the sun and fixed stars, and v/as not wanted for ob- 
serving terrestrial angles, it would be the best way to have none of 
the glasses silvered, but to leave the horizon-glasses intirely trans- 
parent, and to put a red glass for an index-glass of the same matter 
with the darkening glasses, which would reflect light irom the fore- 
surface only. ' • 

p 



314 ReTTiarks on the Hadleifs Quadrant y 

The sun's altitude might also be observed with this instrument, 
either by the fore or back-observation; and the altitude of the moon 
might be taken vi^ith it in the night. But the altitudes of stars could 
not be observed with it, nor the moon's altitude in the day time, which 
would however be no great inconvenience, as these observations might 
be well enough supplied by common quadrants. , 

The following rules for the size of the glasses and the silvering 
them, and the height of the telescope may be of use. The index 
glass and two horizon-glasses should be all of equal height, and even 
with one another in height both at top and bottom. The telescope 
should be moveable parallel to itself nearer to or farther from the 
plane of the quadrant, and the range of its motion should be such 
that its axis when at the lowest station should point about -tV^h of an 
inch lower than the top of the silvering of the horizon-glasses, and 
when at the highest station should point to the height of the middle 
of the unsilvered part of the index-glass. The height of the glasses, 
and the quantity of parts silvered and parts unsilvered, should vary 
according to the aperture of the object-glass, as in the following ta- 
ble ; where the first column of figures shews the dimensions in parts 
of an inch answering to an aperture of the object-glass of T2_.ths of 
an inch in diameter; the second column what answer to an aperture 
of the object-glass of T^ths of an inch in diameter; and the third, 
tvhat are suitable to an aperture of the object-glass of ^^g-ths of an 
inch in diameter. 



hy th& Rev, Dr. Maskelyne. 



115 



Diameter of aperttu'c of obj ect-glasss • • • • 

Height of glasses 

Height of silvered part of index glass 

Height of unsilvered part of di tto 

Height of silvered part of horizon-glasses 
Height of unsilvered part of ditto 



Pafts of an Inch. 



,30 0,40 



,90 1,13 
,50 0,63 
,40 0,50 
,25 0,33 
,6510,80 



0,50 



1,37 
0,77 
0,60 
0,42 
0,95 



If the telescope has a common object-glass, the first aperture of 
Wths of an inch will be most convenient; but if it has an achromatic 
object-glassj one of the other apertures of v^ths or -i^ths of an inch, 
will be most proper. The field of view of the telescope should be 5 
or (5 degrees, and the objects should be rendered as distinct as possible 
throughout the whole field, by applying two eye-glasses to the teles- 
cope. The breadth of the glasses should be determined as usual, 
according to the obliquity with which the rays fall on them and the 
aperture of the object-glass. 

I shall conclude this paper with some easy rules for finding the 
apparent angular distance between any two near land objects by the 
Hadley's quadrant. 

To firid the angular distance between two near objects by the fore- 
observation. Adjust the fore-horizon-glass by the object intended to 
be taken as the direct-object; and the angle measured by the fore- 
observation on the arch of the quadrant between this object and any 
other object seen by reflection will be the true angle between them 
as seen from the centre of the index-glass. But, if the quadrant be 
already well adjusted by a distant object, and you do not chuse to alter 
it by adjusting it by a near one, move the index, and bring the image 

p 2 



Il6 Remarks on the Hadlmfs Quadrant, 

of the near direct object to coincide with the same seen directly, 
and the number of minutes by which (o) of the index stands to the 
right hand of (o) of the quadrant upon the arch of the excess is the 
correction, which added to the angle measured by the arch of the 
quadrant between this direct object and any other object seen by re- 
flection will give the true angular distance between them reduced to 
the centre of the index. 

To Jind the angular, distance between two near objects by the back- 
observation. 

It is supposed that the horizon-glass is truly adjusted ; if it is riot, 
let it be so. Observe the distance of the objects by the back-observa- 
tion, and take the supplement of the degrees and minutes standing 
upon the arch to 180 degrees, which call the instrumental angular 
distance of the objects; this is to be corrected as follows. Keep the 
centre of the quadrant or index-glass in the same place as it had in 
the foregoing observation, and observe the distance between the near 
object, which has been just taken as the direct object, and some dis- 
tant object, twice; by making both objects to be the direct and 
reflected ones alternately, holding the divided arch upwards in one 
case and downwards in the other, still preserving the place of the cen- 
tre of the quadrant. The difference of these two observations will 
be the correction, which added to the instrumental angular distance, 
found as above in the first observation between the first object and 
any other object seen by reflection, will give the true angular distance 
between them reduced to the centre of the index glass. 



by the Rev, Dr. Mashetyne, 117 

I" 

But if you should happen to be in a place where you cannot com- 
mand a convenient distant object, the following method may be used. 

The back- horizon-glass being adjusted, find the instrumental an- 
gular distance between the objects; this is to be corrected by means 
of the following operations. Set up a mark at any convenient dis- 
tance opposite or nearly so to the object which has been taken as the 
direct object; and looking at the direct object move the index of the 
quadrant, and bring the image of the mark to coincide with the di- 
rect object, and read off the degrees and minutes standing on the 
arch of the quadrant, which substract from 180 degrees, if (O) of 
the index falls upon the quadrantal arch; but add to 180 degrees, if 
it falls upon the arch of excess; and you will have the instrumental 
angular distance of the object and mark. Invert the plane of the 
quadrant, taking care at the same time not to change the place of its 
centre, and looking at the same direct object as before, move the in- 
dex of the quadrant, and bring the image of the mark to coincide 
again with the direct object, and read off the degrees and minutes 
standing on the arch, and thence also find the instrumental angular 
distance of the object and mark. Take the sum of this and the for- 
mer instrumental angular distance; half of its difference from 36o° 
will be the correction, which added to the instrumental angular dis- 
tance first found between the same direct object and the other object 
seen by reflection will give the true angular distance between them 
reduced to the centre of the index-glass. 

It is to be observed, that if the mark be set up at the same distance 
from the quadrant as the direct object is, there will be no occasion to 
invert the plane of the quadrant, but the observer need only make 



11§ Remarks on the Hadlei/s Quadrant^ i^c. 

the image of the mark coincide with tlae direct object, then turn him-' 
self half round, and, now taking the mark for the direct object cause 
the image of the former direct object to coincide with the mark, the 
divided arch of the quadrant being kept upwards, and the place of 
the centre of the quadrant remaining also the same; in both cases: 
half the difference of the sum of the two instrumental angles from 
360° will be the correction of the adjustment as before. 

Should only one of the objects be near, and the other remote (that 
is to say, half a mile distant or more) let the distant object be taken 
for the direct one, and the near object for the reflected one; and the 
true distance of the objects as seen from the centre of the index-glass 
will be obtained without requiring any correction, whether it be the 
back or fore-observation that is made use of; only observing, as usual, 
to take the supplement of what is shown upon the arch to 180° in 
the back-observation. 



m 



An Account of an Apparatus applied to the 
Equatorial Instrument for correcting the Errors 
arising from the Refraction in Altitude* By 
Mr, Peter DoUond, Optician; commvmcated to 
the Royal Society hy the Astronmner Royal, 



Read March 4, 1779. 



X HE refraction of the atmosphere occasions the stars or planets to 
appear higher above the horizon than they really are; therefore, a 
correction for this refraction should be made in a vertical direction to 
the horizon. 

The equatorial instrument is so constructed, that thd correction 
cannot be made by the arches or circles which compose it, when the 
star, &c. is in any other vertical arch except that of the meridian ; 
because the declination arch is never in a vertical position but when 
the telescope is in the plane of the meridian. 



120 jiccount of an Apparatus applied (o the Equatorial Instruinent, 

To correct this error, a method of moving the eye-tube which 
contains the wires of the telescope in a vertical direction to the hori- 
zon has been practised; but as the eye -tube is obliged to be turned 
round in order to move it in that direction, in the different oblique 
positions of the instrument, the wires are thereby put out of their 
proper situation in every other ^position of the instrument, except 
when it is in the plane of the meridian; for the equatorial wire 
should always be parallel to the equator, that the star in passing over 
the field of the telescope may move along with it, otherwise one can- 
not judge whether the telescope be set to the proper declination, 
except at the instant the star is brought to the intersection of the 
wires, which is only a momentary observation. 

The method I have now put in practice for correcting the refraction 
of the atmosphere is, by applying two lenses before the object-glass of 
the telescope; one of them convex, and the other concave; both 
ground on spheres of the same radius, which in those I have 
made is thirty feet. The convex lens is round, of the same diameter 
as the object-glass of the telescope, and fixed into a brass frame or 
apparatus, which fits on to the end of the telescope. The concave 
lens is of the same width, but nearly two inches longer than it is 
wide, and is fixed in an oblong frame, which is made to slide on the 
frame that the other lens is fixed into, and close to it. These two lenses 
being wrought on spheres of the same radius, , the refraction of the 
one will be exactly destroyed by that of the other, and the focal 
length of the object-glass, will not be altered by their being applied 
before it: and if the centres of these two lenses coincide with each 



by Mr. Peter Dollond. 121 

other, and also with that of the object-glass, the image of any object 
formed in the telescope will not be moved' or suffer any change in its 
position. But if one of the lenses be moved on the other, in the di- 
rection of a vertical arch^ so as to separate its centre from that of 
the other lens, it will occasion a refraction, and the image will change 
its altitude in the telescope. The Quantity of fhf» rpfrartion will be 
always in proportion to the motion of the lens, so that by a scale of 
equal parts applied to the brass frame, the lens maybe spt to occasion 
a refraction equ^l to the refraction of the atmosphere in any altitude. 
If the concave lens be moved downwards, that is, towards the horizon, 
its refraction will then be in a contrary direction to that of the at- 
mosphere,- and the star will appear in the telescope as if no refraction 
had taken place. 

There is a small circular spirit level fixed on one side of the apparatus, 
which serves to set it in such a position, that the centres of the two 
lenses may be in the plane of a vertical arch. This level is also used 
for adjusting a small quadrant, which is fixed to it, and divided into 
degrees, to shew the elevation of the telescope when directed to the 
star; then the quantity of refraction answering to that altitude may 
be found by the common tables, and the concave lens set accordingly, 
by means of the scale at the side, which is divided into half minutes, 
and, if required, by using a nonius, may be divided into seconds. 

It must be observed, that when a star or planet is but a few degrees 
above the horizon, the refraction of the atmosphere occasions it to be 
considerably coloured. The refraction of the lens acting in a contrary 
direction would exactly correct that colour, if the dissipation of the 

a 



122 jiccount of an jipparatiLS applied to the Equatorial Instrument ^ 

r^ys of light were the same in glass as in air; but as it is greater in 
^lass than in air, the colours occasioned by the refraction of the at-, 
mosphere will be rather more than corrected by those occasioned by 
•the refraction of the lens. 

The following is a drawing of the refraction apparatus, which may 
serve to give a more clear idea of it. 




by Mr. Peter Dollond. 123 

EXPLANATION OF THE PLATE. 

AA. The circular brass tube, which fits on to the end of the telescope, 
BB. The oblong concave lens in its frame, which slides over the fixed 

convex lens. 
c. The circular spirit level, which shews when the oblong lens is in 

a vertical arch. 

D. The quadrant to which the spirit level is fixed, for shewing the 

angular elevation of the telescope. 

E. The milled head fixed to a pinion, by which the whole apparatus is 

turned round on the end of the telescope, in order to set the 
oblong lens in a vertical arch. • ' 

F. Another pinion for setting the quadrant to the angular elevation 

of the telescope. By means of these two pinions the air bub- 
ble must be brought to the middle of the level. 
aa. Is the scale, with divisions answering to minutes and half minutes 
of the refraction occasioned by the concave lens. 




W. M. Thiselton, Printer, Goodge Street, London. 



m